Core

The graph shows the variation with position s of the displacement x of a wave undergoing simple harmonic motion (SHM).

What is the magnitude of the velocity at the displacements X, Y and Z?

The graph shows the variation with position s of the displacement x of a wave undergoing simple harmonic motion (SHM).

What is the magnitude of the velocity at the displacements X, Y and Z?

Unpolarized light of intensity I₀ is incident on a polarizing filter. Light from this filter is incident on a second filter, which has its axis of polarization at 30˚ to that of the first filter.

The value of cos 30˚ is $\frac{\sqrt{3}}{2}$. What is the intensity of the light emerging through the second filter?

A. $\frac{\sqrt{3}}{2}$I₀

B. $\frac{3}{2}$I₀

C. $\frac{3}{4}$I₀

D. $\frac{3}{8}$I₀

Unpolarized light of intensity I₀ is incident on a polarizing filter. Light from this filter is incident on a second filter, which has its axis of polarization at 30˚ to that of the first filter.

The value of cos 30˚ is $\frac{\sqrt{3}}{2}$. What is the intensity of the light emerging through the second filter?

A. $\frac{\sqrt{3}}{2}$I₀

B. $\frac{3}{2}$I₀

C. $\frac{3}{4}$I₀

D. $\frac{3}{8}$I₀

The diagram shows a second harmonic standing wave on a string fixed at both ends.

What is the phase difference, in rad, between the particle at X and the particle at Y?

A. 0

B. $\frac{\pi }{4}$

C. $\frac{\pi }{2}$

D. $\frac{3\pi }{4}$

The diagram shows a second harmonic standing wave on a string fixed at both ends.

What is the phase difference, in rad, between the particle at X and the particle at Y?

A. 0

B. $\frac{\pi }{4}$

C. $\frac{\pi }{2}$

D. $\frac{3\pi }{4}$

Two wires, X and Y, are made from the same metal. The wires are connected in series. The radius of X is twice that of Y. The carrier drift speed in X is v_X and in Y it is v_Y.

What is the value of the ratio $\frac{{\text{v}}_{\text{X}}}{{\text{v}}_{\text{Y}}}$?

A. 0.25

B. 0.50

C. 2.00

D. 4.00

The diagram shows the forces acting on a block resting on an inclined plane. The angle θ is adjusted until the block is just at the point of sliding. R is the normal reaction, W the weight of the block and F the maximum frictional force.

What is the maximum coefficient of static friction between the block and the plane?

A. sin θ

B. cos θ

C. tan θ

D. $\frac{1}{\text{tan}\theta }$

Two wires, X and Y, are made from the same metal. The wires are connected in series. The radius of X is twice that of Y. The carrier drift speed in X is v_X and in Y it is v_Y.

What is the value of the ratio $\frac{{\text{v}}_{\text{X}}}{{\text{v}}_{\text{Y}}}$?

A. 0.25

B. 0.50

C. 2.00

D. 4.00

The diagram shows the forces acting on a block resting on an inclined plane. The angle θ is adjusted until the block is just at the point of sliding. R is the normal reaction, W the weight of the block and F the maximum frictional force.

What is the maximum coefficient of static friction between the block and the plane?

A. sin θ

B. cos θ

C. tan θ

D. $\frac{1}{\text{tan}\theta }$

A system that consists of a single spring stores a total elastic potential energy E_p when a load is added to the spring. Another identical spring connected in parallel is added to the system. The same load is now applied to the parallel springs.

What is the total elastic potential energy stored in the changed system?

A. E_p

B. $\frac{E_p}{2}$

C. $\frac{E_p}{4}$

D. $\frac{E_p}{8}$

A system that consists of a single spring stores a total elastic potential energy E_p when a load is added to the spring. Another identical spring connected in parallel is added to the system. The same load is now applied to the parallel springs.

What is the total elastic potential energy stored in the changed system?

A. E_p

B. $\frac{E_p}{2}$

C. $\frac{E_p}{4}$

D. $\frac{E_p}{8}$

After leaving the snow slope, the girl on the sledge moves over a horizontal region of snow. Explain, with reference to the physical origin of the forces, why the vertical forces on the girl must be in equilibrium as she moves over the horizontal region.

After leaving the snow slope, the girl on the sledge moves over a horizontal region of snow. Explain, with reference to the physical origin of the forces, why the vertical forces on the girl must be in equilibrium as she moves over the horizontal region.

After leaving the snow slope, the girl on the sledge moves over a horizontal region of snow. Explain, with reference to the physical origin of the forces, why the vertical forces on the girl must be in equilibrium as she moves over the horizontal region.

The graph shows the variation with time t of the velocity v of an object undergoing simple harmonic motion (SHM). At which velocity does the displacement from the mean position take a maximum positive value?

When the sledge is moving on the horizontal region of the snow, the girl jumps off the sledge. The girl has no horizontal velocity after the jump. The velocity of the sledge immediately after the girl jumps off is 4.2 m s^–1. The mass of the girl is 55 kg and the mass of the sledge is 5.5 kg. Calculate the speed of the sledge immediately before the girl jumps from it.

The graph shows the variation with time t of the velocity v of an object undergoing simple harmonic motion (SHM). At which velocity does the displacement from the mean position take a maximum positive value?

When the sledge is moving on the horizontal region of the snow, the girl jumps off the sledge. The girl has no horizontal velocity after the jump. The velocity of the sledge immediately after the girl jumps off is 4.2 m s^–1. The mass of the girl is 55 kg and the mass of the sledge is 5.5 kg. Calculate the speed of the sledge immediately before the girl jumps from it.

When the sledge is moving on the horizontal region of the snow, the girl jumps off the sledge. The girl has no horizontal velocity after the jump. The velocity of the sledge immediately after the girl jumps off is 4.2 m s^–1. The mass of the girl is 55 kg and the mass of the sledge is 5.5 kg. Calculate the speed of the sledge immediately before the girl jumps from it.

What is the phase difference, in rad, between the centre of a compression and the centre of a rarefaction for a longitudinal travelling wave?

A. 0

B. $\frac{\pi }{2}$

C. $\pi$

D. $2\pi$

What is the phase difference, in rad, between the centre of a compression and the centre of a rarefaction for a longitudinal travelling wave?

A. 0

B. $\frac{\pi }{2}$

C. $\pi$

D. $2\pi$

The girl chooses to jump so that she lands on loosely-packed snow rather than frozen ice. Outline why she chooses to land on the snow.

The girl chooses to jump so that she lands on loosely-packed snow rather than frozen ice. Outline why she chooses to land on the snow.

The girl chooses to jump so that she lands on loosely-packed snow rather than frozen ice. Outline why she chooses to land on the snow.

The refractive index for light travelling from medium X to medium Y is $\frac{4}{3}$. The refractive index for light travelling from medium Y to medium Z is $\frac{3}{5}$. What is the refractive index for light travelling from medium X to medium Z?

A. $\frac{4}{5}$

B. $\frac{15}{12}$

C. $\frac{5}{4}$

D. $\frac{29}{15}$

The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.

The refractive index for light travelling from medium X to medium Y is $\frac{4}{3}$. The refractive index for light travelling from medium Y to medium Z is $\frac{3}{5}$. What is the refractive index for light travelling from medium X to medium Z?

A. $\frac{4}{5}$

B. $\frac{15}{12}$

C. $\frac{5}{4}$

D. $\frac{29}{15}$

The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.

The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.

A pipe of fixed length is closed at one end. What is $\frac{\text{third harmonic frequency of pipe}}{\text{first harmonic frequency of pipe}}$?

A. $\frac{1}{5}$

B. $\frac{1}{3}$

C. 3

D. 5

Show that the acceleration of the sledge is about –2 m s^–2.

A pipe of fixed length is closed at one end. What is $\frac{\text{third harmonic frequency of pipe}}{\text{first harmonic frequency of pipe}}$?

A. $\frac{1}{5}$

B. $\frac{1}{3}$

C. 3

D. 5

State the unit for the quantity represented by the gradient in your answer to (b)(i).

State the unit for the quantity represented by the gradient in your answer to (b)(i).

State the unit for the quantity represented by the gradient in your answer to (b)(i).

Show that the acceleration of the sledge is about –2 m s^–2.

Show that the acceleration of the sledge is about –2 m s^–2.

Calculate the distance along the slope at which the sledge stops moving. Assume that the coefficient of dynamic friction is constant.

Using an appropriate error calculation, justify the number of significant figures that should be used for your answer to (c)(i).

Using an appropriate error calculation, justify the number of significant figures that should be used for your answer to (c)(i).

Using an appropriate error calculation, justify the number of significant figures that should be used for your answer to (c)(i).

Show that the gradient of the graph is equal to $\frac{1}{e}$.

Show that the gradient of the graph is equal to $\frac{1}{e}$.

Show that the gradient of the graph is equal to $\frac{1}{e}$.

Calculate the distance along the slope at which the sledge stops moving. Assume that the coefficient of dynamic friction is constant.

Calculate the distance along the slope at which the sledge stops moving. Assume that the coefficient of dynamic friction is constant.

The resistance of the carbon film is 82 Ω. The resistivity of carbon is 4.1 x 10^–5 Ω m. Calculate the length l of the film.

The resistance of the carbon film is 82 Ω. The resistivity of carbon is 4.1 x 10^–5 Ω m. Calculate the length l of the film.

The resistance of the carbon film is 82 Ω. The resistivity of carbon is 4.1 x 10^–5 Ω m. Calculate the length l of the film.

A student measures the radius r of a sphere with an absolute uncertainty Δr. What is the fractional uncertainty in the volume of the sphere?

A.     ${\left(\frac{\mathrm{\Delta }r}{r}\right)}^3$

B.     $3\frac{\mathrm{\Delta }r}{r}$

C.     $4\pi \frac{\mathrm{\Delta }r}{r}$

D.     $4\pi {\left(\frac{\mathrm{\Delta }r}{r}\right)}^3$

A satellite X of mass m orbits the Earth with a period T. What will be the orbital period of satellite Y of mass 2m occupying the same orbit as X?

A. $\frac{T}{2}$

B. T

C. $\sqrt{2T}$

D. 2T

The film must dissipate a power less than 1500 W from each square metre of its surface to avoid damage. Calculate the maximum allowable current for the resistor.

A satellite X of mass m orbits the Earth with a period T. What will be the orbital period of satellite Y of mass 2m occupying the same orbit as X?

A. $\frac{T}{2}$

B. T

C. $\sqrt{2T}$

D. 2T

The film must dissipate a power less than 1500 W from each square metre of its surface to avoid damage. Calculate the maximum allowable current for the resistor.

The film must dissipate a power less than 1500 W from each square metre of its surface to avoid damage. Calculate the maximum allowable current for the resistor.

A student measures the radius r of a sphere with an absolute uncertainty Δr. What is the fractional uncertainty in the volume of the sphere?

A.     ${\left(\frac{\mathrm{\Delta }r}{r}\right)}^3$

B.     $3\frac{\mathrm{\Delta }r}{r}$

C.     $4\pi \frac{\mathrm{\Delta }r}{r}$

D.     $4\pi {\left(\frac{\mathrm{\Delta }r}{r}\right)}^3$

The current direction is now changed so that charge flows vertically through the film.

Deduce, without calculation, the change in the resistance.

The current direction is now changed so that charge flows vertically through the film.

Deduce, without calculation, the change in the resistance.

The current direction is now changed so that charge flows vertically through the film.

Deduce, without calculation, the change in the resistance.

Calculate the speed of light inside the ice cube.

Calculate the speed of light inside the ice cube.

Calculate the speed of light inside the ice cube.

Show that no light emerges from side AB.

The energy density of a substance can be calculated by multiplying its specific energy with which quantity?

A. mass

B. volume

C. $\frac{\text{mass}}{\text{volume}}$

D. $\frac{\text{volume}}{\text{mass}}$

Show that no light emerges from side AB.

Show that no light emerges from side AB.

The energy density of a substance can be calculated by multiplying its specific energy with which quantity?

A. mass

B. volume

C. $\frac{\text{mass}}{\text{volume}}$

D. $\frac{\text{volume}}{\text{mass}}$

An object falls from rest from a height h close to the surface of the Moon. The Moon has no atmosphere.

When the object has fallen to height $\frac{h}{4}$ above the surface, what is

                                      $\frac{\text{kinetic energy of the object at }\frac{h}{4}}{\text{gravitational potential energy of the object at }h}$?

A.     $\frac{3}{4}$

B.     $\frac{4}{3}$

C.     $\frac{9}{16}$

D.     $\frac{16}{9}$

A black body emits radiation with its greatest intensity at a wavelength of I_max. The surface temperature of the black body doubles without any other change occurring. What is the wavelength at which the greatest intensity of radiation is emitted?

A. I_max

B. $\frac{\text{I}{}_{\text{max}}}{\text{2}}$

C. $\frac{\text{I}{}_{\text{max}}}{\text{4}}$

D. $\frac{\text{I}{}_{\text{max}}}{\text{16}}$

A black body emits radiation with its greatest intensity at a wavelength of I_max. The surface temperature of the black body doubles without any other change occurring. What is the wavelength at which the greatest intensity of radiation is emitted?

A. I_max

B. $\frac{\text{I}{}_{\text{max}}}{\text{2}}$

C. $\frac{\text{I}{}_{\text{max}}}{\text{4}}$

D. $\frac{\text{I}{}_{\text{max}}}{\text{16}}$

An object falls from rest from a height h close to the surface of the Moon. The Moon has no atmosphere.

When the object has fallen to height $\frac{h}{4}$ above the surface, what is

                                      $\frac{\text{kinetic energy of the object at }\frac{h}{4}}{\text{gravitational potential energy of the object at }h}$?

A.     $\frac{3}{4}$

B.     $\frac{4}{3}$

C.     $\frac{9}{16}$

D.     $\frac{16}{9}$

between B and C.

Determine the energy required to melt all of the ice from –20 °C to water at a temperature of 0 °C.

Specific latent heat of fusion of ice  = 330 kJ kg^–1
Specific heat capacity of ice            = 2.1 kJ kg^–1 k^–1
Density of ice                                = 920 kg m^–3

Determine the energy required to melt all of the ice from –20 °C to water at a temperature of 0 °C.

Specific latent heat of fusion of ice  = 330 kJ kg^–1
Specific heat capacity of ice            = 2.1 kJ kg^–1 k^–1
Density of ice                                = 920 kg m^–3

Determine the energy required to melt all of the ice from –20 °C to water at a temperature of 0 °C.

Specific latent heat of fusion of ice  = 330 kJ kg^–1
Specific heat capacity of ice            = 2.1 kJ kg^–1 k^–1
Density of ice                                = 920 kg m^–3

Outline the difference between the molecular structure of a solid and a liquid.

Outline the difference between the molecular structure of a solid and a liquid.

Outline the difference between the molecular structure of a solid and a liquid.

between B and C.

Determine the orbital period for the satellite.

Mass of Earth = 6.0 x 10²⁴ kg

between B and C.

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

Determine the orbital period for the satellite.

Mass of Earth = 6.0 x 10²⁴ kg

Determine the orbital period for the satellite.

Mass of Earth = 6.0 x 10²⁴ kg

Determine the mean temperature of the Earth.

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

Determine the mean temperature of the Earth.

Determine the mean temperature of the Earth.

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

At position B the rope starts to extend. Calculate the speed of the block at position B.

An object is moving in a straight line. A force F and a resistive force f act on the object along the straight line.

Both forces act for a time t.

What is the rate of change of momentum with time of the object during time t ?

A.     F + f 

B.     F – f

C.     (F + f )t

D.     (F – f )t 

An object is moving in a straight line. A force F and a resistive force f act on the object along the straight line.

Both forces act for a time t.

What is the rate of change of momentum with time of the object during time t ?

A.     F + f 

B.     F – f

C.     (F + f )t

D.     (F – f )t 

At position B the rope starts to extend. Calculate the speed of the block at position B.

What are the units of the ratio $\frac{\text{specific heat capacity of copper}}{\text{specific latent heat of vaporization of copper}}$?

A.     no units

B.     k

C.     k^–1

D.     k^–2

At position B the rope starts to extend. Calculate the speed of the block at position B.

Determine the magnitude of the average resultant force acting on the block between B and C.

Determine the magnitude of the average resultant force acting on the block between B and C.

What are the units of the ratio $\frac{\text{specific heat capacity of copper}}{\text{specific latent heat of vaporization of copper}}$?

A.     no units

B.     k

C.     k^–1

D.     k^–2

A sealed cylinder of length l and cross-sectional area A contains N molecules of an ideal gas at kelvin temperature T.

What is the force acting on the area of the cylinder marked A due to the gas?

A.     $\frac{NRT}{l}$

B.     $\frac{NRT}{lA}$

C.     $\frac{N{k}_{B}T}{lA}$

D.     $\frac{N{k}_{B}T}{l}$

Determine the magnitude of the average resultant force acting on the block between B and C.

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

A sealed cylinder of length l and cross-sectional area A contains N molecules of an ideal gas at kelvin temperature T.

What is the force acting on the area of the cylinder marked A due to the gas?

A.     $\frac{NRT}{l}$

B.     $\frac{NRT}{lA}$

C.     $\frac{N{k}_{B}T}{lA}$

D.     $\frac{N{k}_{B}T}{l}$

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

between A and B.

between A and B.

between A and B.

between B and C.

A particle is displaced from rest and released at time t = 0. It performs simple harmonic motion (SHM). Which graph shows the variation with time of the kinetic energy E_k of the particle?

between B and C.

A particle is displaced from rest and released at time t = 0. It performs simple harmonic motion (SHM). Which graph shows the variation with time of the kinetic energy E_k of the particle?

between B and C.

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

Calculate the pressure of the gas.

Calculate the pressure of the gas.

Calculate the pressure of the gas.

Calculate, in kg, the mass of the gas.

Two resistors X and Y are made of uniform cylinders of the same material. X and Y are connected in series. X and Y are of equal length and the diameter of Y is twice the diameter of X.

The resistance of Y is R.

What is the resistance of this series combination?

A.     $\frac{5R}{4}$

B.     $\frac{3R}{2}$

C.     3R

D.     5R

Calculate, in kg, the mass of the gas.

Calculate, in kg, the mass of the gas.

Calculate the average kinetic energy of the particles of the gas.

Two resistors X and Y are made of uniform cylinders of the same material. X and Y are connected in series. X and Y are of equal length and the diameter of Y is twice the diameter of X.

The resistance of Y is R.

What is the resistance of this series combination?

A.     $\frac{5R}{4}$

B.     $\frac{3R}{2}$

C.     3R

D.     5R

An object of mass m at the end of a string of length r moves in a vertical circle at a constant angular speed ω.

What is the tension in the string when the object is at the bottom of the circle?

A.     m(ω²r + g)

B.     m(ω²r – g)

C.     mg(ω²r + 1)

D.     mg(ω²r – 1)

Calculate the average kinetic energy of the particles of the gas.

Calculate the average kinetic energy of the particles of the gas.

Calculate the average kinetic energy of the particles of the gas.

Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.

An object of mass m at the end of a string of length r moves in a vertical circle at a constant angular speed ω.

What is the tension in the string when the object is at the bottom of the circle?

A.     m(ω²r + g)

B.     m(ω²r – g)

C.     mg(ω²r + 1)

D.     mg(ω²r – 1)

Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.

Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.

A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed.

Which Feynman diagram shows beta-plus (β⁺) decay?

A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed.

A weight W is tied to a trolley of mass M by a light string passing over a frictionless pulley. The trolley has an acceleration a on a frictionless table. The acceleration due to gravity is g.

What is W ?

A.    $\frac{Mag}{(g-a)}$

B.    $\frac{Mag}{(g+a)}$

C.    $\frac{Ma}{(g-a)}$

D.     $\frac{Ma}{(g+a)}$

A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed.

The wavelength of the beam as observed on Earth is 633.0 nm. The separation between a dark and a bright fringe on the screen is 4.50 mm. Calculate D.

A weight W is tied to a trolley of mass M by a light string passing over a frictionless pulley. The trolley has an acceleration a on a frictionless table. The acceleration due to gravity is g.

What is W ?

A.    $\frac{Mag}{(g-a)}$

B.    $\frac{Mag}{(g+a)}$

C.    $\frac{Ma}{(g-a)}$

D.     $\frac{Ma}{(g+a)}$

Which Feynman diagram shows beta-plus (β⁺) decay?

The average binding energy per nucleon of the ${}_8^{15}\text{O}$ nucleus is 7.5 MeV. What is the total energy required to separate the nucleons of one nucleus of ${}_8^{15}\text{O}$?

A.     53 MeV

B.     60 MeV

C.     113 MeV

D.     173 MeV

The wavelength of the beam as observed on Earth is 633.0 nm. The separation between a dark and a bright fringe on the screen is 4.50 mm. Calculate D.

The wavelength of the beam as observed on Earth is 633.0 nm. The separation between a dark and a bright fringe on the screen is 4.50 mm. Calculate D.

Calculate the wavelength of the light in water.

Calculate the wavelength of the light in water.

The average binding energy per nucleon of the ${}_8^{15}\text{O}$ nucleus is 7.5 MeV. What is the total energy required to separate the nucleons of one nucleus of ${}_8^{15}\text{O}$?

A.     53 MeV

B.     60 MeV

C.     113 MeV

D.     173 MeV

Two pure samples of radioactive nuclides X and Y have the same initial number of atoms. The half-life of X is $T_{\frac{1}{2}}$.

After a time equal to 4 half-lives of X the ratio $\frac{\text{number of atoms of X}}{\text{number of atoms of Y}}$ is $\frac{1}{8}$.

What is the half-life of Y?

A.     $0.25T_{\frac{1}{2}}$

B.     $0.5T_{\frac{1}{2}}$

C.     $3T_{\frac{1}{2}}$

D.     $4T_{\frac{1}{2}}$

Calculate the wavelength of the light in water.

State two ways in which the intensity pattern on the screen changes.

State two ways in which the intensity pattern on the screen changes.

Two pure samples of radioactive nuclides X and Y have the same initial number of atoms. The half-life of X is $T_{\frac{1}{2}}$.

After a time equal to 4 half-lives of X the ratio $\frac{\text{number of atoms of X}}{\text{number of atoms of Y}}$ is $\frac{1}{8}$.

What is the half-life of Y?

A.     $0.25T_{\frac{1}{2}}$

B.     $0.5T_{\frac{1}{2}}$

C.     $3T_{\frac{1}{2}}$

D.     $4T_{\frac{1}{2}}$

State two ways in which the intensity pattern on the screen changes.

Calculate the resistance of the conductor.

What is equivalent to $\frac{\text{specific energy of a fuel}}{\text{energy density of a fuel}}$?

A.     density of the fuel

B.     $\frac{1}{\text{density of the fuel}}$

C.     $\frac{\text{energy stored in the fuel}}{\text{density of the fuel}}$

D.     $\frac{\text{density of the fuel}}{\text{energy stored in the fuel}}$

The graph shows how the temperature of a liquid varies with time when energy is supplied to the liquid at a constant rate P. The gradient of the graph is K and the liquid has a specific heat capacity c.

What is the mass of the liquid?

A.     $\frac{P}{cK}$

B.     $\frac{PK}{c}$

C.     $\frac{Pc}{K}$

D.     $\frac{cK}{P}$

Calculate the resistance of the conductor.

The graph shows how the temperature of a liquid varies with time when energy is supplied to the liquid at a constant rate P. The gradient of the graph is K and the liquid has a specific heat capacity c.

What is the mass of the liquid?

A.     $\frac{P}{cK}$

B.     $\frac{PK}{c}$

C.     $\frac{Pc}{K}$

D.     $\frac{cK}{P}$

Calculate the resistance of the conductor.

Calculate the drift speed v of the electrons in the conductor in cm s^–1. State your answer to an appropriate number of significant figures.

What is equivalent to $\frac{\text{specific energy of a fuel}}{\text{energy density of a fuel}}$?

A.     density of the fuel

B.     $\frac{1}{\text{density of the fuel}}$

C.     $\frac{\text{energy stored in the fuel}}{\text{density of the fuel}}$

D.     $\frac{\text{density of the fuel}}{\text{energy stored in the fuel}}$

Calculate the drift speed v of the electrons in the conductor in cm s^–1. State your answer to an appropriate number of significant figures.

Calculate the drift speed v of the electrons in the conductor in cm s^–1. State your answer to an appropriate number of significant figures.

State the direction of the magnetic field.

State the direction of the magnetic field.

What is true about the acceleration of a particle that is oscillating with simple harmonic motion (SHM)?

A.     It is in the opposite direction to its velocity

B.     It is decreasing when the potential energy is increasing

C.     It is proportional to the frequency of the oscillation

D.     It is at a minimum when the velocity is at a maximum

State the direction of the magnetic field.

Calculate, in N, the magnitude of the magnetic force acting on the electron.

What is true about the acceleration of a particle that is oscillating with simple harmonic motion (SHM)?

A.     It is in the opposite direction to its velocity

B.     It is decreasing when the potential energy is increasing

C.     It is proportional to the frequency of the oscillation

D.     It is at a minimum when the velocity is at a maximum

At position B the rope starts to extend. Calculate the speed of the block at position B.

Calculate, in N, the magnitude of the magnetic force acting on the electron.

At position B the rope starts to extend. Calculate the speed of the block at position B.

At position B the rope starts to extend. Calculate the speed of the block at position B.

Calculate, in N, the magnitude of the magnetic force acting on the electron.

Explain why the electron moves at constant speed.

Explain why the electron moves at constant speed.

Determine the magnitude of the average resultant force acting on the block between B and C.

Explain why the electron moves at constant speed.

Determine the magnitude of the average resultant force acting on the block between B and C.

Determine the magnitude of the average resultant force acting on the block between B and C.

Explain why the electron moves on a circular path.

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

Explain why the electron moves on a circular path.

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

Explain why the electron moves on a circular path.

Identify the missing information for this decay.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

Identify the missing information for this decay.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

Identify the missing information for this decay.

On the graph, sketch how the number of boron nuclei in the sample varies with time.

between A and B.

On the graph, sketch how the number of boron nuclei in the sample varies with time.

between A and B.

between A and B.

On the graph, sketch how the number of boron nuclei in the sample varies with time.

After 4.3 × 10⁶ years,

$$\frac{\text{number of produced boron nuclei}}{\text{number of remaining beryllium nuclei}}=7.$$

Show that the half-life of beryllium-10 is 1.4 × 10⁶ years.

The speed of sound in air is 340 m s^–1 and in water it is 1500 m s^–1.

The wavefronts make an angle θ with the surface of the water. Determine the maximum angle, θ_max, at which the sound can enter water. Give your answer to the correct number of significant figures.

After 4.3 × 10⁶ years,

$$\frac{\text{number of produced boron nuclei}}{\text{number of remaining beryllium nuclei}}=7.$$

Show that the half-life of beryllium-10 is 1.4 × 10⁶ years.

After 4.3 × 10⁶ years,

$$\frac{\text{number of produced boron nuclei}}{\text{number of remaining beryllium nuclei}}=7.$$

Show that the half-life of beryllium-10 is 1.4 × 10⁶ years.

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10¹¹ atoms of beryllium-10. State the number of remaining beryllium-10 nuclei in the sample after 2.8 × 10⁶ years.

The speed of sound in air is 340 m s^–1 and in water it is 1500 m s^–1.

The wavefronts make an angle θ with the surface of the water. Determine the maximum angle, θ_max, at which the sound can enter water. Give your answer to the correct number of significant figures.

The speed of sound in air is 340 m s^–1 and in water it is 1500 m s^–1.

The wavefronts make an angle θ with the surface of the water. Determine the maximum angle, θ_max, at which the sound can enter water. Give your answer to the correct number of significant figures.

Draw lines on the diagram to complete wavefronts A and B in water for θ < θ_max.

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10¹¹ atoms of beryllium-10. State the number of remaining beryllium-10 nuclei in the sample after 2.8 × 10⁶ years.

Draw lines on the diagram to complete wavefronts A and B in water for θ < θ_max.

Draw lines on the diagram to complete wavefronts A and B in water for θ < θ_max.

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10¹¹ atoms of beryllium-10. State the number of remaining beryllium-10 nuclei in the sample after 2.8 × 10⁶ years.

State what is meant by thermal radiation.

State what is meant by the emf of a cell.

Element X decays through a series of alpha (α) and beta minus (β^–) emissions. Which series of emissions results in an isotope of X?

A.     1α and 2β^–

B.     1α and 4β^–

C.     2α and 2β^–

D.     2α and 3β^–

State what is meant by thermal radiation.

Element X decays through a series of alpha (α) and beta minus (β^–) emissions. Which series of emissions results in an isotope of X?

A.     1α and 2β^–

B.     1α and 4β^–

C.     2α and 2β^–

D.     2α and 3β^–

State what is meant by the emf of a cell.

State what is meant by the emf of a cell.

State what is meant by thermal radiation.

Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.

Show that the resistance of the wire AC is 28 Ω.

Show that the resistance of the wire AC is 28 Ω.

Show that the resistance of the wire AC is 28 Ω.

Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.

Determine E.

Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

Determine E.

Determine E.

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

A wind turbine has a power output p when the wind speed is v. The efficiency of the wind turbine does not change. What is the wind speed at which the power output is $\frac{p}{2}$?

A.     $\frac{v}{4}$

B.     $\frac{v}{\sqrt{8}}$

C.     $\frac{v}{2}$

D.     $\frac{v}{\sqrt[3]{2}}$

Estimate the specific energy of water in this storage system, giving an appropriate unit for your answer.

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

Derive the units of intensity in terms of fundamental SI units.

Estimate the specific energy of water in this storage system, giving an appropriate unit for your answer.

Estimate the specific energy of water in this storage system, giving an appropriate unit for your answer.

A wind turbine has a power output p when the wind speed is v. The efficiency of the wind turbine does not change. What is the wind speed at which the power output is $\frac{p}{2}$?

A.     $\frac{v}{4}$

B.     $\frac{v}{\sqrt{8}}$

C.     $\frac{v}{2}$

D.     $\frac{v}{\sqrt[3]{2}}$

Derive the units of intensity in terms of fundamental SI units.

Three gases in the atmosphere are

          I.     carbon dioxide (CO₂)

          II.     dinitrogen monoxide (N₂O)

          III.     oxygen (O₂).

Which of these are considered to be greenhouse gases?

A.     I and II only

B.     I and III only

C.     II and III only

D.     I, II and III

Show that the average rate at which the gravitational potential energy of the water decreases is 2.5 GW.

Derive the units of intensity in terms of fundamental SI units.

Draw on the graph the line of best fit for the data.

Show that the average rate at which the gravitational potential energy of the water decreases is 2.5 GW.

Show that the average rate at which the gravitational potential energy of the water decreases is 2.5 GW.

The storage system produces 1.8 GW of electrical power. Determine the overall efficiency of the storage system.

Three gases in the atmosphere are

          I.     carbon dioxide (CO₂)

          II.     dinitrogen monoxide (N₂O)

          III.     oxygen (O₂).

Which of these are considered to be greenhouse gases?

A.     I and II only

B.     I and III only

C.     II and III only

D.     I, II and III

Mars and Earth act as black bodies. The $\frac{\text{power radiated by Mars}}{\text{power radiated by the Earth}}=p$ and $\frac{\text{absolute mean temperature of the surface of Mars}}{\text{absolute mean temperature of the surface of the Earth}}=t$.

What is the value of $\frac{\text{radius of Mars}}{\text{radius of the Earth}}$?

A.     $\frac{p}{t^4}$

B.     $\frac{\sqrt{p}}{t^2}$

C.     $\frac{t^4}{p}$

D.     $\frac{t^2}{\sqrt{p}}$

Draw on the graph the line of best fit for the data.

Mars and Earth act as black bodies. The $\frac{\text{power radiated by Mars}}{\text{power radiated by the Earth}}=p$ and $\frac{\text{absolute mean temperature of the surface of Mars}}{\text{absolute mean temperature of the surface of the Earth}}=t$.

What is the value of $\frac{\text{radius of Mars}}{\text{radius of the Earth}}$?

A.     $\frac{p}{t^4}$

B.     $\frac{\sqrt{p}}{t^2}$

C.     $\frac{t^4}{p}$

D.     $\frac{t^2}{\sqrt{p}}$

The storage system produces 1.8 GW of electrical power. Determine the overall efficiency of the storage system.

The storage system produces 1.8 GW of electrical power. Determine the overall efficiency of the storage system.

Draw on the graph the line of best fit for the data.

Write down the time taken for one oscillation when B = 0.005 T with its absolute uncertainty.

After the upper lake is emptied it must be refilled with water from the lower lake and this requires energy. Suggest how the operators of this storage system can still make a profit.

Write down the time taken for one oscillation when B = 0.005 T with its absolute uncertainty.

After the upper lake is emptied it must be refilled with water from the lower lake and this requires energy. Suggest how the operators of this storage system can still make a profit.

After the upper lake is emptied it must be refilled with water from the lower lake and this requires energy. Suggest how the operators of this storage system can still make a profit.

Write down the time taken for one oscillation when B = 0.005 T with its absolute uncertainty.

A student forms a hypothesis that the period of one oscillation P is given by:

$$P=\frac{K}{\sqrt{B}}$$

where K is a constant.

Determine the value of K using the point for which B = 0.005 T.

State the uncertainty in K to an appropriate number of significant figures. 

A student forms a hypothesis that the period of one oscillation P is given by:

$$P=\frac{K}{\sqrt{B}}$$

where K is a constant.

Determine the value of K using the point for which B = 0.005 T.

State the uncertainty in K to an appropriate number of significant figures. 

A student forms a hypothesis that the period of one oscillation P is given by:

$$P=\frac{K}{\sqrt{B}}$$

where K is a constant.

Determine the value of K using the point for which B = 0.005 T.

State the uncertainty in K to an appropriate number of significant figures. 

State the unit of K.

Rutherford constructed a model of the atom based on the results of the alpha particle scattering experiment. Describe this model.

State the direction of the resultant force on the ball.

State the unit of K.

Rutherford constructed a model of the atom based on the results of the alpha particle scattering experiment. Describe this model.

Rutherford constructed a model of the atom based on the results of the alpha particle scattering experiment. Describe this model.

State the unit of K.

The student plots a graph to show how P² varies with $\frac{1}{B}$ for the data.

Sketch the shape of the expected line of best fit on the axes below assuming that the relationship $P=\frac{K}{\sqrt{B}}$ is verified. You do not have to put numbers on the axes.

State what is meant by the binding energy of a nucleus.

The student plots a graph to show how P² varies with $\frac{1}{B}$ for the data.

Sketch the shape of the expected line of best fit on the axes below assuming that the relationship $P=\frac{K}{\sqrt{B}}$ is verified. You do not have to put numbers on the axes.

The student plots a graph to show how P² varies with $\frac{1}{B}$ for the data.

Sketch the shape of the expected line of best fit on the axes below assuming that the relationship $P=\frac{K}{\sqrt{B}}$ is verified. You do not have to put numbers on the axes.

State how the value of K can be obtained from the graph.

State what is meant by the binding energy of a nucleus.

State what is meant by the binding energy of a nucleus.

State the direction of the resultant force on the ball.

State the direction of the resultant force on the ball.

State how the value of K can be obtained from the graph.

Show that the energy released in the β^– decay of rhodium is about 3 MeV.

State how the value of K can be obtained from the graph.

Draw a suitable circuit diagram that would enable the internal resistance to be determined.

Draw a suitable circuit diagram that would enable the internal resistance to be determined.

Show that the energy released in the β^– decay of rhodium is about 3 MeV.

Show that the energy released in the β^– decay of rhodium is about 3 MeV.

Draw a suitable circuit diagram that would enable the internal resistance to be determined.

It is noticed that the resistor gets warmer. Explain how this would affect the calculated value of the internal resistance.

It is noticed that the resistor gets warmer. Explain how this would affect the calculated value of the internal resistance.

On the diagram, construct an arrow of the correct length to represent the weight of the ball.

It is noticed that the resistor gets warmer. Explain how this would affect the calculated value of the internal resistance.

Outline how using a variable resistance could improve the accuracy of the value found for the internal resistance.

Draw a labelled arrow to complete the Feynman diagram.

Outline how using a variable resistance could improve the accuracy of the value found for the internal resistance.

Outline how using a variable resistance could improve the accuracy of the value found for the internal resistance.

Draw a labelled arrow to complete the Feynman diagram.

Draw a labelled arrow to complete the Feynman diagram.

Identify particle V.

Identify particle V.

Identify particle V.

On the diagram, construct an arrow of the correct length to represent the weight of the ball.

On the diagram, construct an arrow of the correct length to represent the weight of the ball.

Show that the magnitude of the net force F on the ball is given by the following equation.

                                          $$F=\frac{mg}{\tan \theta }$$

Show that the magnitude of the net force F on the ball is given by the following equation.

                                          $$F=\frac{mg}{\tan \theta }$$

Show that the magnitude of the net force F on the ball is given by the following equation.

                                          $$F=\frac{mg}{\tan \theta }$$

Determine the distance fallen, in m, by the centre of mass of the sphere including an estimate of the absolute uncertainty in your answer.

Determine the distance fallen, in m, by the centre of mass of the sphere including an estimate of the absolute uncertainty in your answer.

Determine the distance fallen, in m, by the centre of mass of the sphere including an estimate of the absolute uncertainty in your answer.

Using the following equation

$$\text{acceleration due to gravity}=\frac{2\times \text{distance fallen by centre of mass of sphere}}{{\text{(measured time to fall)}}^{\text{2}}}$$

calculate, for these data, the acceleration due to gravity including an estimate of the absolute uncertainty in your answer.

Using the following equation

$$\text{acceleration due to gravity}=\frac{2\times \text{distance fallen by centre of mass of sphere}}{{\text{(measured time to fall)}}^{\text{2}}}$$

calculate, for these data, the acceleration due to gravity including an estimate of the absolute uncertainty in your answer.

Using the following equation

$$\text{acceleration due to gravity}=\frac{2\times \text{distance fallen by centre of mass of sphere}}{{\text{(measured time to fall)}}^{\text{2}}}$$

calculate, for these data, the acceleration due to gravity including an estimate of the absolute uncertainty in your answer.

This relationship can also be written as follows.

$$\frac{1}{\sqrt{I}}=Kx+KC$$

Show that $K=2\sqrt{\frac{\pi }{P}}$.

This relationship can also be written as follows.

$$\frac{1}{\sqrt{I}}=Kx+KC$$

Show that $K=2\sqrt{\frac{\pi }{P}}$.

This relationship can also be written as follows.

$$\frac{1}{\sqrt{I}}=Kx+KC$$

Show that $K=2\sqrt{\frac{\pi }{P}}$.

Estimate C.

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

Estimate C.

Estimate C.

Determine P, to the correct number of significant figures including its unit.

Determine P, to the correct number of significant figures including its unit.

Determine P, to the correct number of significant figures including its unit.

Explain the disadvantage that a graph of I versus $\frac{1}{x^2}$ has for the analysis in (b)(i) and (b)(ii).

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

An ion of charge +Q moves vertically upwards through a small distance s in a uniform vertical electric field. The electric field has a strength E and its direction is shown in the diagram.

What is the electric potential difference between the initial and final position of the ion?

A.     $\frac{EQ}{s}$

B.     EQs

C.     Es

D.     $\frac{E}{s}$

Explain the disadvantage that a graph of I versus $\frac{1}{x^2}$ has for the analysis in (b)(i) and (b)(ii).

Explain the disadvantage that a graph of I versus $\frac{1}{x^2}$ has for the analysis in (b)(i) and (b)(ii).

An ion of charge +Q moves vertically upwards through a small distance s in a uniform vertical electric field. The electric field has a strength E and its direction is shown in the diagram.

What is the electric potential difference between the initial and final position of the ion?

A.     $\frac{EQ}{s}$

B.     EQs

C.     Es

D.     $\frac{E}{s}$

Describe the effect of F on the linear speed of the wheel.

Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.

When an electric cell of negligible internal resistance is connected to a resistor of resistance 4R, the power dissipated in the resistor is P.

What is the power dissipated in a resistor of resistance value R when it is connected to the same cell?

A.     $\frac{P}{4}$

B.     P

C.     4P

D.     16P

When an electric cell of negligible internal resistance is connected to a resistor of resistance 4R, the power dissipated in the resistor is P.

What is the power dissipated in a resistor of resistance value R when it is connected to the same cell?

A.     $\frac{P}{4}$

B.     P

C.     4P

D.     16P

Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.

Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.

Describe the effect of F on the linear speed of the wheel.

Describe the effect of F on the linear speed of the wheel.

Determine, in kJ, the total kinetic energy of the particles of the gas.

Determine, in kJ, the total kinetic energy of the particles of the gas.

Determine, in kJ, the total kinetic energy of the particles of the gas.

Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.

Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.

Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.

A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed.

A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed.

A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed.

State what is meant by an ideal gas.

write down the momentum of the neutrino.

State what is meant by an ideal gas.

State what is meant by an ideal gas.

Calculate the number of atoms in the gas.

Outline why the beam has to be coherent in order for the fringes to be visible.

Outline why the beam has to be coherent in order for the fringes to be visible.

Outline why the beam has to be coherent in order for the fringes to be visible.

write down the momentum of the neutrino.

Calculate the number of atoms in the gas.

Calculate the number of atoms in the gas.

write down the momentum of the neutrino.

Calculate, in J, the internal energy of the gas.

Calculate, in J, the internal energy of the gas.

Calculate, in J, the internal energy of the gas.

The wavelength of the beam as observed on Earth is 633.0 nm. The separation between a dark and a bright fringe on the screen is 4.50 mm. Calculate D.

The wavelength of the beam as observed on Earth is 633.0 nm. The separation between a dark and a bright fringe on the screen is 4.50 mm. Calculate D.

The wavelength of the beam as observed on Earth is 633.0 nm. The separation between a dark and a bright fringe on the screen is 4.50 mm. Calculate D.

Calculate, in Pa, the new pressure of the gas.

Calculate, in Pa, the new pressure of the gas.

Calculate, in Pa, the new pressure of the gas.

Explain, in terms of molecular motion, this change in pressure.

Explain, in terms of molecular motion, this change in pressure.

Explain, in terms of molecular motion, this change in pressure.

Calculate the resistance of the conductor.

Calculate the resistance of the conductor.

Calculate the resistance of the conductor.

Calculate the drift speed v of the electrons in the conductor in cm s^–1.

Calculate the drift speed v of the electrons in the conductor in cm s^–1.

Calculate the drift speed v of the electrons in the conductor in cm s^–1.

A ball of mass m collides with a vertical wall with an initial horizontal speed u and rebounds with a horizontal speed v. The graph shows the variation of the speed of the ball with time.

What is the magnitude of the mean net force on the ball during the collision?

A.     $\frac{m(u-v)}{(t_2+t_1)}$

B.     $\frac{m(u-v)}{(t_2-t_1)}$

C.     $\frac{m(u+v)}{(t_2+t_1)}$

D.     $\frac{m(u+v)}{(t_2-t_1)}$

Determine the electric field strength E.

Determine the electric field strength E.

Determine the electric field strength E.

Outline how the standing wave is formed.

A ball of mass m collides with a vertical wall with an initial horizontal speed u and rebounds with a horizontal speed v. The graph shows the variation of the speed of the ball with time.

What is the magnitude of the mean net force on the ball during the collision?

A.     $\frac{m(u-v)}{(t_2+t_1)}$

B.     $\frac{m(u-v)}{(t_2-t_1)}$

C.     $\frac{m(u+v)}{(t_2+t_1)}$

D.     $\frac{m(u+v)}{(t_2-t_1)}$

Outline how the standing wave is formed.

Outline how the standing wave is formed.

Show that $\frac{v}{E}=\frac{1}{ne\rho }$.

Show that $\frac{v}{E}=\frac{1}{ne\rho }$.

Show that $\frac{v}{E}=\frac{1}{ne\rho }$.

Q and R are two rigid containers of volume 3V and V respectively containing molecules of the same ideal gas initially at the same temperature. The gas pressures in Q and R are p and 3p respectively. The containers are connected through a valve of negligible volume that is initially closed.

The valve is opened in such a way that the temperature of the gases does not change. What is the change of pressure in Q?

A.     +p

B.     $\frac{+p}{2}$

C.     $\frac{-p}{2}$

D.     –p

Identify the missing information for this decay.

Draw an arrow on the diagram to represent the direction of motion of the molecule at X.

Q and R are two rigid containers of volume 3V and V respectively containing molecules of the same ideal gas initially at the same temperature. The gas pressures in Q and R are p and 3p respectively. The containers are connected through a valve of negligible volume that is initially closed.

The valve is opened in such a way that the temperature of the gases does not change. What is the change of pressure in Q?

A.     +p

B.     $\frac{+p}{2}$

C.     $\frac{-p}{2}$

D.     –p

Draw an arrow on the diagram to represent the direction of motion of the molecule at X.

Draw an arrow on the diagram to represent the direction of motion of the molecule at X.

A string stretched between two fixed points sounds its second harmonic at frequency f.

Which expression, where n is an integer, gives the frequencies of harmonics that have a node at the centre of the string?

A.     $\frac{n+1}{2}f$

B.     nf

C.     2nf

D.     (2n + 1)f

Label a position N that is a node of the standing wave.

Identify the missing information for this decay.

Identify the missing information for this decay.

A string stretched between two fixed points sounds its second harmonic at frequency f.

Which expression, where n is an integer, gives the frequencies of harmonics that have a node at the centre of the string?

A.     $\frac{n+1}{2}f$

B.     nf

C.     2nf

D.     (2n + 1)f

On the graph, sketch how the number of boron nuclei in the sample varies with time.

Label a position N that is a node of the standing wave.

Label a position N that is a node of the standing wave.

The speed of sound is 340 m s^–1 and the length of the pipe is 0.30 m. Calculate, in Hz, the frequency of the sound.

The speed of sound is 340 m s^–1 and the length of the pipe is 0.30 m. Calculate, in Hz, the frequency of the sound.

The speed of sound is 340 m s^–1 and the length of the pipe is 0.30 m. Calculate, in Hz, the frequency of the sound.

On the graph, sketch how the number of boron nuclei in the sample varies with time.

On the graph, sketch how the number of boron nuclei in the sample varies with time.

After 4.3 × 10⁶ years,

$$\frac{\text{number of produced boron nuclei}}{\text{number of remaining beryllium nuclei}}=7.$$

Show that the half-life of beryllium-10 is 1.4 × 10⁶ years.

After 4.3 × 10⁶ years,

$$\frac{\text{number of produced boron nuclei}}{\text{number of remaining beryllium nuclei}}=7.$$

Show that the half-life of beryllium-10 is 1.4 × 10⁶ years.

After 4.3 × 10⁶ years,

$$\frac{\text{number of produced boron nuclei}}{\text{number of remaining beryllium nuclei}}=7.$$

Show that the half-life of beryllium-10 is 1.4 × 10⁶ years.

An object of mass m moves in a horizontal circle of radius r with a constant speed v. What is the rate at which work is done by the centripetal force?

A.     $\frac{m{v}^3}{r}$

B.     $\frac{m{v}^3}{2\pi r}$

C.     $\frac{m{v}^3}{4\pi r}$

D.     zero

State what is meant by thermal radiation.

State what is meant by thermal radiation.

State what is meant by thermal radiation.

An object of mass m moves in a horizontal circle of radius r with a constant speed v. What is the rate at which work is done by the centripetal force?

A.     $\frac{m{v}^3}{r}$

B.     $\frac{m{v}^3}{2\pi r}$

C.     $\frac{m{v}^3}{4\pi r}$

D.     zero

Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.

Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.

Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.

State the direction of the resultant force on the ball.

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

State the direction of the resultant force on the ball.

State the direction of the resultant force on the ball.

The temperature in the laboratory is higher than the temperature of the ice sample. Describe one other energy transfer that occurs between the ice sample and the laboratory.

The temperature in the laboratory is higher than the temperature of the ice sample. Describe one other energy transfer that occurs between the ice sample and the laboratory.

The temperature in the laboratory is higher than the temperature of the ice sample. Describe one other energy transfer that occurs between the ice sample and the laboratory.

On the diagram, construct an arrow of the correct length to represent the weight of the ball.

On the diagram, construct an arrow of the correct length to represent the weight of the ball.

On the diagram, construct an arrow of the correct length to represent the weight of the ball.

An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.

State what is meant by an ideal gas.

An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.

An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.

Show that the magnitude of the net force F on the ball is given by the following equation.

                                          $$F=\frac{mg}{\tan \theta }$$

State what is meant by an ideal gas.

Show that the magnitude of the net force F on the ball is given by the following equation.

                                          $$F=\frac{mg}{\tan \theta }$$

Show that the magnitude of the net force F on the ball is given by the following equation.

                                          $$F=\frac{mg}{\tan \theta }$$

State what is meant by an ideal gas.

Calculate the number of atoms in the gas.

Calculate the number of atoms in the gas.

Calculate the number of atoms in the gas.

Calculate, in J, the internal energy of the gas.

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

Calculate, in J, the internal energy of the gas.

Calculate, in J, the internal energy of the gas.

Calculate, in Pa, the new pressure of the gas.

Calculate, in Pa, the new pressure of the gas.

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

Calculate, in Pa, the new pressure of the gas.

Explain, in terms of molecular motion, this change in pressure.

Explain, in terms of molecular motion, this change in pressure.

Explain, in terms of molecular motion, this change in pressure.

Outline how the standing wave is formed.

Outline how the standing wave is formed.

Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.

Outline how the standing wave is formed.

Draw an arrow on the diagram to represent the direction of motion of the molecule at X.

Draw an arrow on the diagram to represent the direction of motion of the molecule at X.

Draw an arrow on the diagram to represent the direction of motion of the molecule at X.

Label a position N that is a node of the standing wave.

Label a position N that is a node of the standing wave.

Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.

Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.

Label a position N that is a node of the standing wave.

The speed of sound is 340 m s^–1 and the length of the pipe is 0.30 m. Calculate, in Hz, the frequency of the sound.

The speed of sound is 340 m s^–1 and the length of the pipe is 0.30 m. Calculate, in Hz, the frequency of the sound.

The speed of sound is 340 m s^–1 and the length of the pipe is 0.30 m. Calculate, in Hz, the frequency of the sound.

The speed of sound in air is 340 m s^–1 and in water it is 1500 m s^–1.

The wavefronts make an angle θ with the surface of the water. Determine the maximum angle, θ_max, at which the sound can enter water. Give your answer to the correct number of significant figures.

The speed of sound in air is 340 m s^–1 and in water it is 1500 m s^–1.

The wavefronts make an angle θ with the surface of the water. Determine the maximum angle, θ_max, at which the sound can enter water. Give your answer to the correct number of significant figures.

Outline why the ball will perform simple harmonic oscillations about the equilibrium position.

The speed of sound in air is 340 m s^–1 and in water it is 1500 m s^–1.

The wavefronts make an angle θ with the surface of the water. Determine the maximum angle, θ_max, at which the sound can enter water. Give your answer to the correct number of significant figures.

Draw lines on the diagram to complete wavefronts A and B in water for θ < θ_max.

Draw lines on the diagram to complete wavefronts A and B in water for θ < θ_max.

Draw lines on the diagram to complete wavefronts A and B in water for θ < θ_max.

Outline why the ball will perform simple harmonic oscillations about the equilibrium position.

Outline why the ball will perform simple harmonic oscillations about the equilibrium position.

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.

A mass m attached to a string of length R moves in a vertical circle with a constant speed. The tension in the string at the top of the circle is T. What is the kinetic energy of the mass at the top of the circle?

A.   $\frac{R\left(T+mg\right)}{2}$

B.   $\frac{R\left(T-mg\right)}{2}$

C.   $\frac{Rmg}{2}$

D.   $\frac{R\left(2T+mg\right)}{2}$

State what is meant by the emf of a cell.

State what is meant by the emf of a cell.

State what is meant by the emf of a cell.

Show that the resistance of the wire AC is 28 Ω.

A mass m attached to a string of length R moves in a vertical circle with a constant speed. The tension in the string at the top of the circle is T. What is the kinetic energy of the mass at the top of the circle?

A.   $\frac{R\left(T+mg\right)}{2}$

B.   $\frac{R\left(T-mg\right)}{2}$

C.   $\frac{Rmg}{2}$

D.   $\frac{R\left(2T+mg\right)}{2}$

Show that the resistance of the wire AC is 28 Ω.

Show that the resistance of the wire AC is 28 Ω.

Determine E.

Determine E.

Determine E.

Cell X is replaced by a second cell of identical emf E but with internal resistance 2.0 Ω. Comment on the length of AC for which the current in the second cell is zero.

Cell X is replaced by a second cell of identical emf E but with internal resistance 2.0 Ω. Comment on the length of AC for which the current in the second cell is zero.

Cell X is replaced by a second cell of identical emf E but with internal resistance 2.0 Ω. Comment on the length of AC for which the current in the second cell is zero.

State what is meant by gravitational field strength.

State what is meant by gravitational field strength.

State what is meant by gravitational field strength.

The mass of the asteroid is 6.2 × 10¹² kg. Calculate the gravitational force experienced by the planet when the asteroid is at point P.

The mass of the asteroid is 6.2 × 10¹² kg. Calculate the gravitational force experienced by the planet when the asteroid is at point P.

The mass of the asteroid is 6.2 × 10¹² kg. Calculate the gravitational force experienced by the planet when the asteroid is at point P.

L is a point source of light. The intensity of the light at a distance 2$x$ from L is I. What is the intensity at a distance 3$x$ from L?

A.   $\frac{4}{9}$I

B.   $\frac{2}{3}$I

C.   $\frac{3}{2}$I

D.   $\frac{9}{4}$I

L is a point source of light. The intensity of the light at a distance 2$x$ from L is I. What is the intensity at a distance 3$x$ from L?

A.   $\frac{4}{9}$I

B.   $\frac{2}{3}$I

C.   $\frac{3}{2}$I

D.   $\frac{9}{4}$I

Calculate, in A, the average current during the discharge.

Calculate, in A, the average current during the discharge.

Calculate, in A, the average current during the discharge.

Show that the speed v of an electron in the hydrogen atom is related to the radius r of the orbit by the expression

$$v=\sqrt{\frac{k{e}^2}{m_{\text{e}}r}}$$

where k is the Coulomb constant.

Show that the speed v of an electron in the hydrogen atom is related to the radius r of the orbit by the expression

$$v=\sqrt{\frac{k{e}^2}{m_{\text{e}}r}}$$

where k is the Coulomb constant.

Show that the speed v of an electron in the hydrogen atom is related to the radius r of the orbit by the expression

$$v=\sqrt{\frac{k{e}^2}{m_{\text{e}}r}}$$

where k is the Coulomb constant.

Suggest why the β^– decay is followed by the emission of a gamma ray photon.

A compressed spring is used to launch an object along a horizontal frictionless surface. When the spring is compressed through a distance $x$ and released, the object leaves the spring at speed $v$. What is the distance through which the spring must be compressed for the object to leave the spring at $\frac{v}{2}$?

A.   $\frac{x}{4}$

B.   $\frac{x}{2}$

C.   $\frac{x}{\sqrt{2}}$

D.   $x\sqrt{2}$

Suggest why the β^– decay is followed by the emission of a gamma ray photon.

Suggest why the β^– decay is followed by the emission of a gamma ray photon.

The following decay is observed.

μ⁻ → e⁻ + v_μ + X

What is particle X?

A.   γ

B.   $\overline{v}$_e

C.   Z⁰

D.   v_e

The following decay is observed.

μ⁻ → e⁻ + v_μ + X

What is particle X?

A.   γ

B.   $\overline{v}$_e

C.   Z⁰

D.   v_e

A compressed spring is used to launch an object along a horizontal frictionless surface. When the spring is compressed through a distance $x$ and released, the object leaves the spring at speed $v$. What is the distance through which the spring must be compressed for the object to leave the spring at $\frac{v}{2}$?

A.   $\frac{x}{4}$

B.   $\frac{x}{2}$

C.   $\frac{x}{\sqrt{2}}$

D.   $x\sqrt{2}$

Two point charges Q₁ and Q₂ are one metre apart. The graph shows the variation of electric potential V with distance $x$ from Q₁.

What is $\frac{Q_1}{Q_2}$?

A.   $\frac{1}{16}$

B.   $\frac{1}{4}$

C.   4

D.   16

A ball of mass m collides with a wall and bounces back in a straight line. The ball loses 75 % of the initial energy during the collision. The speed before the collision is v.

What is the magnitude of the impulse on the ball by the wall?

A.   $\left(1-\frac{\sqrt{3}}{2}\right)mv$

B.   $\frac{1}{2}mv$

C.   $\frac{5}{4}mv$

D.   $\frac{3}{2}mv$

Determine the magnitude of the average decelerating force that the ground exerts on the egg.

Two point charges Q₁ and Q₂ are one metre apart. The graph shows the variation of electric potential V with distance $x$ from Q₁.

What is $\frac{Q_1}{Q_2}$?

A.   $\frac{1}{16}$

B.   $\frac{1}{4}$

C.   4

D.   16

Determine the magnitude of the average decelerating force that the ground exerts on the egg.

Determine the magnitude of the average decelerating force that the ground exerts on the egg.

A ball of mass m collides with a wall and bounces back in a straight line. The ball loses 75 % of the initial energy during the collision. The speed before the collision is v.

What is the magnitude of the impulse on the ball by the wall?

A.   $\left(1-\frac{\sqrt{3}}{2}\right)mv$

B.   $\frac{1}{2}mv$

C.   $\frac{5}{4}mv$

D.   $\frac{3}{2}mv$

Determine the initial acceleration of the spacecraft.

A container is filled with a mixture of helium and oxygen at the same temperature. The molar mass of helium is 4 g mol^–1 and that of oxygen is 32 g mol^–1.

What is the ratio $\frac{\text{average speed of helium molecules}}{\text{average speed of oxygen molecules}}$?

A.   $\frac{1}{8}$

B.   $\frac{1}{\sqrt{8}}$

C.   $\sqrt{8}$

D.   8

A container is filled with a mixture of helium and oxygen at the same temperature. The molar mass of helium is 4 g mol^–1 and that of oxygen is 32 g mol^–1.

What is the ratio $\frac{\text{average speed of helium molecules}}{\text{average speed of oxygen molecules}}$?

A.   $\frac{1}{8}$

B.   $\frac{1}{\sqrt{8}}$

C.   $\sqrt{8}$

D.   8

Container X contains 1.0 mol of an ideal gas. Container Y contains 2.0 mol of the ideal gas. Y has four times the volume of X. The pressure in X is twice that in Y.

What is $\frac{\text{temperature of gas in X}}{\text{temperature of gas in Y}}$?

A.   $\frac{1}{4}$

B.   $\frac{1}{2}$

C.   1

D.   2

Container X contains 1.0 mol of an ideal gas. Container Y contains 2.0 mol of the ideal gas. Y has four times the volume of X. The pressure in X is twice that in Y.

What is $\frac{\text{temperature of gas in X}}{\text{temperature of gas in Y}}$?

A.   $\frac{1}{4}$

B.   $\frac{1}{2}$

C.   1

D.   2

The speed of sound c for longitudinal waves in air is given by

$c=\sqrt{\frac{K}{\rho }}$

where ρ is the density of the air and K is a constant.

A student measures f to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m^–3. Determine, in kg m^–1 s^–2, the value of K for air.

Determine the initial acceleration of the spacecraft.

The speed of sound c for longitudinal waves in air is given by

$c=\sqrt{\frac{K}{\rho }}$

where ρ is the density of the air and K is a constant.

A student measures f to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m^–3. Determine, in kg m^–1 s^–2, the value of K for air.

The speed of sound c for longitudinal waves in air is given by

$c=\sqrt{\frac{K}{\rho }}$

where ρ is the density of the air and K is a constant.

A student measures f to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m^–3. Determine, in kg m^–1 s^–2, the value of K for air.

A particle moving in a circle completes 5 revolutions in 3 s. What is the frequency?

A.   $\frac{3}{5}$Hz

B.   $\frac{5}{3}$Hz

C.   $\frac{3\pi }{5}$Hz

D.   $\frac{5\pi }{3}$Hz

Determine the initial acceleration of the spacecraft.

Estimate the maximum speed of the spacecraft.

A particle moving in a circle completes 5 revolutions in 3 s. What is the frequency?

A.   $\frac{3}{5}$Hz

B.   $\frac{5}{3}$Hz

C.   $\frac{3\pi }{5}$Hz

D.   $\frac{5\pi }{3}$Hz

Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.

Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.

Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.

Estimate the maximum speed of the spacecraft.

Determine the energy of a photon of blue light (435nm) emitted in the hydrogen spectrum.

The graphs show the variation of the displacement y of a medium with distance $x$ and with time t for a travelling wave.

What is the speed of the wave?

A.   0.6 m s^–1

B.   0.8 m s^–1

C.   600 m s^–1

D.   800 m s^–1

Estimate the maximum speed of the spacecraft.

Outline why the ions are likely to spread out.

The graphs show the variation of the displacement y of a medium with distance $x$ and with time t for a travelling wave.

What is the speed of the wave?

A.   0.6 m s^–1

B.   0.8 m s^–1

C.   600 m s^–1

D.   800 m s^–1

Determine the energy of a photon of blue light (435nm) emitted in the hydrogen spectrum.

Determine the energy of a photon of blue light (435nm) emitted in the hydrogen spectrum.

Identify, with an arrow labelled B on the diagram, the transition in the hydrogen spectrum that gives rise to the photon with the energy in (a).

Outline why the ions are likely to spread out.

Identify, with an arrow labelled B on the diagram, the transition in the hydrogen spectrum that gives rise to the photon with the energy in (a).

Identify, with an arrow labelled B on the diagram, the transition in the hydrogen spectrum that gives rise to the photon with the energy in (a).

Explain your answer to (b).

In a double-slit experiment, a source of monochromatic red light is incident on slits S₁ and S₂ separated by a distance $d$. A screen is located at distance $x$ from the slits. A pattern with fringe spacing $y$ is observed on the screen.

Three changes are possible for this arrangement

I.    increasing $x$

II.   increasing $d$

III.  using green monochromatic light instead of red.

Which changes will cause a decrease in fringe spacing $y$?

A.   I and II only

B.   I and III only

C.   II and III only

D.   I, II, and III

In a double-slit experiment, a source of monochromatic red light is incident on slits S₁ and S₂ separated by a distance $d$. A screen is located at distance $x$ from the slits. A pattern with fringe spacing $y$ is observed on the screen.

Three changes are possible for this arrangement

I.    increasing $x$

II.   increasing $d$

III.  using green monochromatic light instead of red.

Which changes will cause a decrease in fringe spacing $y$?

A.   I and II only

B.   I and III only

C.   II and III only

D.   I, II, and III

Outline why the ions are likely to spread out.

Two strings of lengths L₁ and L₂ are fixed at both ends. The wavespeed is the same for both strings. They both vibrate at the same frequency. L₁ vibrates at its first harmonic. L₂ vibrates at its third harmonic.

What is $\frac{L_1}{L_2}$?

A.   $\frac{1}{3}$

B.   1

C.   2

D.   3

Two strings of lengths L₁ and L₂ are fixed at both ends. The wavespeed is the same for both strings. They both vibrate at the same frequency. L₁ vibrates at its first harmonic. L₂ vibrates at its third harmonic.

What is $\frac{L_1}{L_2}$?

A.   $\frac{1}{3}$

B.   1

C.   2

D.   3

Explain your answer to (b).

Explain your answer to (b).

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Two copper wires X and Y are connected in series. The diameter of Y is double that of X. The drift speed in X is v. What is the drift speed in Y?

A.   $\frac{v}{4}$

B.   $\frac{v}{2}$

C.   2v

D.   4v

Two copper wires X and Y are connected in series. The diameter of Y is double that of X. The drift speed in X is v. What is the drift speed in Y?

A.   $\frac{v}{4}$

B.   $\frac{v}{2}$

C.   2v

D.   4v

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

A combination of four identical resistors each of resistance R are connected to a source of emf ε of negligible internal resistance. What is the current in the resistor X?

A.   $\frac{\epsilon }{5R}$

B.   $\frac{3\epsilon }{10R}$

C.   $\frac{2\epsilon }{5R}$

D.   $\frac{3\epsilon }{5R}$

Distinguish between the internal energy of the oxygen at the boiling point when it is in its liquid phase and when it is in its gas phase.

Distinguish between the internal energy of the oxygen at the boiling point when it is in its liquid phase and when it is in its gas phase.

Distinguish between the internal energy of the oxygen at the boiling point when it is in its liquid phase and when it is in its gas phase.

A combination of four identical resistors each of resistance R are connected to a source of emf ε of negligible internal resistance. What is the current in the resistor X?

A.   $\frac{\epsilon }{5R}$

B.   $\frac{3\epsilon }{10R}$

C.   $\frac{2\epsilon }{5R}$

D.   $\frac{3\epsilon }{5R}$

Determine the initial acceleration of the spacecraft.

Calculate the volume of the oxygen produced in one second when it is allowed to expand to a pressure of 0.11 MPa and to reach a temperature of 260 K.

Determine the initial acceleration of the spacecraft.

Calculate the volume of the oxygen produced in one second when it is allowed to expand to a pressure of 0.11 MPa and to reach a temperature of 260 K.

Calculate the volume of the oxygen produced in one second when it is allowed to expand to a pressure of 0.11 MPa and to reach a temperature of 260 K.

Determine the initial acceleration of the spacecraft.

(i) Estimate the maximum speed of the spacecraft.

(ii) Outline why the answer to (i) is an estimate.

(i) Estimate the maximum speed of the spacecraft.

(ii) Outline why the answer to (i) is an estimate.

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

(i) Estimate the maximum speed of the spacecraft.

(ii) Outline why the answer to (i) is an estimate.

Outline why the ions are likely to spread out.

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

Outline why the ions are likely to spread out.

Two isolated point particles of mass 4M and 9M are separated by a distance 1 m. A point particle of mass M is placed a distance $x$ from the particle of mass 9M. The net gravitational force on M is zero.

What is $x$?

A.   $\frac{4}{13}$m

B.   $\frac{2}{5}$m

C.   $\frac{3}{5}$m

D.   $\frac{9}{13}$m

Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.

Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.

Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.

Outline why the ions are likely to spread out.

Two isolated point particles of mass 4M and 9M are separated by a distance 1 m. A point particle of mass M is placed a distance $x$ from the particle of mass 9M. The net gravitational force on M is zero.

What is $x$?

A.   $\frac{4}{13}$m

B.   $\frac{2}{5}$m

C.   $\frac{3}{5}$m

D.   $\frac{9}{13}$m

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.

Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.

Copper (${}_{29}^{64}\text{Cu}$) decays to nickel (${}_{28}^{64}\text{Ni}$). What are the particles emitted and the particle that mediates the interaction?

Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.

Copper (${}_{29}^{64}\text{Cu}$) decays to nickel (${}_{28}^{64}\text{Ni}$). What are the particles emitted and the particle that mediates the interaction?

Show that the kinetic energy of the egg just before impact is about 0.6 J.

The following interaction is proposed between a proton and a pion.

p⁺ + $\pi$^– → K^– + $\pi$⁺

The quark content of the $\pi$^– is ūd and the quark content of the K^– is ūs.

Three conservation rules are considered

I.   baryon number

II.  charge

III. strangeness.

Which conservation rules are violated in this interaction?

A.   I and II only

B.   I and III only

C.   II and III only

D.   I, II and III

${}_{15}^{32}\text{P}$ undergoes beta-minus (β^–) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.

The following interaction is proposed between a proton and a pion.

p⁺ + $\pi$^– → K^– + $\pi$⁺

The quark content of the $\pi$^– is ūd and the quark content of the K^– is ūs.

Three conservation rules are considered

I.   baryon number

II.  charge

III. strangeness.

Which conservation rules are violated in this interaction?

A.   I and II only

B.   I and III only

C.   II and III only

D.   I, II and III

Show that the kinetic energy of the egg just before impact is about 0.6 J.

Show that the kinetic energy of the egg just before impact is about 0.6 J.

The egg comes to rest in a time of 55 ms. Determine the magnitude of the average decelerating force that the ground exerts on the egg.

${}_{15}^{32}\text{P}$ undergoes beta-minus (β^–) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.

The egg comes to rest in a time of 55 ms. Determine the magnitude of the average decelerating force that the ground exerts on the egg.

The egg comes to rest in a time of 55 ms. Determine the magnitude of the average decelerating force that the ground exerts on the egg.

${}_{15}^{32}\text{P}$ undergoes beta-minus (β^–) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.

A photovoltaic panel of area S has an efficiency of 20 %. A second photovoltaic panel has an efficiency of 15 %. What is the area of the second panel so that both panels produce the same power under the same conditions?

A.   $\frac{S}{3}$

B.   $\frac{3S}{4}$

C.   $\frac{5S}{4}$

D.   $\frac{4S}{3}$

A photovoltaic panel of area S has an efficiency of 20 %. A second photovoltaic panel has an efficiency of 15 %. What is the area of the second panel so that both panels produce the same power under the same conditions?

A.   $\frac{S}{3}$

B.   $\frac{3S}{4}$

C.   $\frac{5S}{4}$

D.   $\frac{4S}{3}$

Sketch, on the diagram, the variation of displacement of the air molecules with distance along the pipe when t = $\frac{3}{4f}$.

Sketch, on the diagram, the variation of displacement of the air molecules with distance along the pipe when t = $\frac{3}{4f}$.

Sketch, on the diagram, the variation of displacement of the air molecules with distance along the pipe when t = $\frac{3}{4f}$.

The speed of sound c for longitudinal waves in air is given by

$c=\sqrt{\frac{K}{\rho }}$

where ρ is the density of the air and K is a constant.

A student measures f to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m^–3. Determine the value of K for air. State your answer with the appropriate fundamental (SI) unit.

Mars has a mass of 6.4 × 10²³ kg. Show that, for Mars, k is about 9 × 10^–13s²m^–3.

The speed of sound c for longitudinal waves in air is given by

$c=\sqrt{\frac{K}{\rho }}$

where ρ is the density of the air and K is a constant.

A student measures f to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m^–3. Determine the value of K for air. State your answer with the appropriate fundamental (SI) unit.

The speed of sound c for longitudinal waves in air is given by

$c=\sqrt{\frac{K}{\rho }}$

where ρ is the density of the air and K is a constant.

A student measures f to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m^–3. Determine the value of K for air. State your answer with the appropriate fundamental (SI) unit.

Mars has a mass of 6.4 × 10²³ kg. Show that, for Mars, k is about 9 × 10^–13s²m^–3.

Mars has a mass of 6.4 × 10²³ kg. Show that, for Mars, k is about 9 × 10^–13s²m^–3.

The time taken for Mars to revolve on its axis is 8.9 × 10⁴ s. Calculate, in m s^–1, the orbital speed of the satellite.

Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.

The time taken for Mars to revolve on its axis is 8.9 × 10⁴ s. Calculate, in m s^–1, the orbital speed of the satellite.

Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.

Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.

The time taken for Mars to revolve on its axis is 8.9 × 10⁴ s. Calculate, in m s^–1, the orbital speed of the satellite.

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Determine the energy of a photon of blue light (435nm) emitted in the hydrogen spectrum.

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Determine the energy of a photon of blue light (435nm) emitted in the hydrogen spectrum.

Determine the energy of a photon of blue light (435nm) emitted in the hydrogen spectrum.

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

Identify, with an arrow labelled B on the diagram, the transition in the hydrogen spectrum that gives rise to the photon with the energy in (a)(i).

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

Identify, with an arrow labelled B on the diagram, the transition in the hydrogen spectrum that gives rise to the photon with the energy in (a)(i).

Identify, with an arrow labelled B on the diagram, the transition in the hydrogen spectrum that gives rise to the photon with the energy in (a)(i).

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

Explain your answer to (a)(ii).

Explain your answer to (a)(ii).

Explain your answer to (a)(ii).

Distinguish between the internal energy of the oxygen at the boiling point when it is in its liquid phase and when it is in its gas phase.

Distinguish between the internal energy of the oxygen at the boiling point when it is in its liquid phase and when it is in its gas phase.

Distinguish between the internal energy of the oxygen at the boiling point when it is in its liquid phase and when it is in its gas phase.

Calculate the volume of the oxygen produced in one second when it is allowed to expand to a pressure of 0.11 MPa and to reach a temperature of –13 °C.

Calculate the volume of the oxygen produced in one second when it is allowed to expand to a pressure of 0.11 MPa and to reach a temperature of –13 °C.

Calculate the volume of the oxygen produced in one second when it is allowed to expand to a pressure of 0.11 MPa and to reach a temperature of –13 °C.

State the unit of c.

State the unit of c.

State the unit of c.

A student wants to determine the angular speed ω of a rotating object. The period T is 0.50 s ±5 %. The angular speed ω is

$$\omega =\frac{2\pi }{T}$$ 

What is the percentage uncertainty of ω?

A. 0.2 %

B. 2.5 %

C. 5 %

D. 10 %

Calculate the average force exerted by the racquet on the ball.

A student wants to determine the angular speed ω of a rotating object. The period T is 0.50 s ±5 %. The angular speed ω is

$$\omega =\frac{2\pi }{T}$$ 

What is the percentage uncertainty of ω?

A. 0.2 %

B. 2.5 %

C. 5 %

D. 10 %

Suggest whether the data are consistent with the theoretical prediction.

A student models the relationship between the pressure p of a gas and its temperature T as p = $x$ + $y$T.

The units of p are pascal and the units of T are kelvin. What are the fundamental SI units of $x$ and $y$?

Calculate the average force exerted by the racquet on the ball.

Calculate the average force exerted by the racquet on the ball.

Suggest whether the data are consistent with the theoretical prediction.

Suggest whether the data are consistent with the theoretical prediction.

Calculate the average power delivered to the ball during the impact.

A student models the relationship between the pressure p of a gas and its temperature T as p = $x$ + $y$T.

The units of p are pascal and the units of T are kelvin. What are the fundamental SI units of $x$ and $y$?

Calculate the average power delivered to the ball during the impact.

Calculate the average power delivered to the ball during the impact.

Calculate the time it takes the tennis ball to reach the net.

A student suggests that to get a more accurate value of L_v the experiment should be performed twice using different heating rates. With voltage and current V₁, I₁ the mass of water that vaporized in time t is m₁. With voltage and current V₂, I₂ the mass of water that vaporized in time t is m₂. The student now uses the expression

$$L_v=\frac{\left(V_1{I}_1-V_2{I}_2\right)t}{m_1-m_2}$$

to calculate L_v. Suggest, by reference to heat losses, why this is an improvement.

A student suggests that to get a more accurate value of L_v the experiment should be performed twice using different heating rates. With voltage and current V₁, I₁ the mass of water that vaporized in time t is m₁. With voltage and current V₂, I₂ the mass of water that vaporized in time t is m₂. The student now uses the expression

$$L_v=\frac{\left(V_1{I}_1-V_2{I}_2\right)t}{m_1-m_2}$$

to calculate L_v. Suggest, by reference to heat losses, why this is an improvement.

A student suggests that to get a more accurate value of L_v the experiment should be performed twice using different heating rates. With voltage and current V₁, I₁ the mass of water that vaporized in time t is m₁. With voltage and current V₂, I₂ the mass of water that vaporized in time t is m₂. The student now uses the expression

$$L_v=\frac{\left(V_1{I}_1-V_2{I}_2\right)t}{m_1-m_2}$$

to calculate L_v. Suggest, by reference to heat losses, why this is an improvement.

Calculate the time it takes the tennis ball to reach the net.

Calculate the time it takes the tennis ball to reach the net.

Show that the tennis ball passes over the net.

Show that the tennis ball passes over the net.

Show that the tennis ball passes over the net.

Determine the speed of the tennis ball as it strikes the ground.

Show that the time taken for the battery to discharge is about 3 × 10³ s.

Determine the speed of the tennis ball as it strikes the ground.

Determine the speed of the tennis ball as it strikes the ground.

Show that the time taken for the battery to discharge is about 3 × 10³ s.

The mass of a helium atom is 6.6 × 10^-27 kg. Estimate the average speed of the helium atoms in the container.

Show that the time taken for the battery to discharge is about 3 × 10³ s.

The mass of a helium atom is 6.6 × 10^-27 kg. Estimate the average speed of the helium atoms in the container.

The mass of a helium atom is 6.6 × 10^-27 kg. Estimate the average speed of the helium atoms in the container.

Show that the number of helium atoms in the container is 4 × 10²⁰.

Show that the number of helium atoms in the container is 4 × 10²⁰.

Show that the number of helium atoms in the container is 4 × 10²⁰.

Calculate the ratio $\frac{\text{volume of helium atoms}}{\text{volume of helium gas}}$.

Calculate the ratio $\frac{\text{volume of helium atoms}}{\text{volume of helium gas}}$.

Calculate the ratio $\frac{\text{volume of helium atoms}}{\text{volume of helium gas}}$.

A ball is thrown upwards at an angle to the horizontal. Air resistance is negligible. Which statement about the motion of the ball is correct?

A. The acceleration of the ball changes during its flight.

B. The velocity of the ball changes during its flight.

C. The acceleration of the ball is zero at the highest point.

D. The velocity of the ball is zero at the highest point.

Discuss, by reference to the kinetic model of an ideal gas and the answer to (c)(i), whether the assumption that helium behaves as an ideal gas is justified.

Discuss, by reference to the kinetic model of an ideal gas and the answer to (c)(i), whether the assumption that helium behaves as an ideal gas is justified.

Discuss, by reference to the kinetic model of an ideal gas and the answer to (c)(i), whether the assumption that helium behaves as an ideal gas is justified.

Friction and air resistance act on the bicycle and the girl when they move. Assume that all the energy is transferred from the battery to the electric motor. Determine the total average resistive force that acts on the bicycle and the girl.

Particle P in the metal sheet performs simple harmonic oscillations. When the displacement of P is 3.2 μm the magnitude of its acceleration is 7.9 m s^-2. Calculate the magnitude of the acceleration of P when its displacement is 2.3 μm.

Particle P in the metal sheet performs simple harmonic oscillations. When the displacement of P is 3.2 μm the magnitude of its acceleration is 7.9 m s^-2. Calculate the magnitude of the acceleration of P when its displacement is 2.3 μm.

Particle P in the metal sheet performs simple harmonic oscillations. When the displacement of P is 3.2 μm the magnitude of its acceleration is 7.9 m s^-2. Calculate the magnitude of the acceleration of P when its displacement is 2.3 μm.

A ball is thrown upwards at an angle to the horizontal. Air resistance is negligible. Which statement about the motion of the ball is correct?

A. The acceleration of the ball changes during its flight.

B. The velocity of the ball changes during its flight.

C. The acceleration of the ball is zero at the highest point.

D. The velocity of the ball is zero at the highest point.

An object of mass m is sliding down a ramp at constant speed. During the motion it travels a distance $x$ along the ramp and falls through a vertical distance h. The coefficient of dynamic friction between the ramp and the object is μ. What is the total energy transferred into thermal energy when the object travels distance $x$?

A. mgh

B. mgx

C. μmgh

D. μmgx

Friction and air resistance act on the bicycle and the girl when they move. Assume that all the energy is transferred from the battery to the electric motor. Determine the total average resistive force that acts on the bicycle and the girl.

An object of mass m is sliding down a ramp at constant speed. During the motion it travels a distance $x$ along the ramp and falls through a vertical distance h. The coefficient of dynamic friction between the ramp and the object is μ. What is the total energy transferred into thermal energy when the object travels distance $x$?

A. mgh

B. mgx

C. μmgh

D. μmgx

The wave is incident at point Q on the metal–air boundary. The wave makes an angle of 54° with the normal at Q. The speed of sound in the metal is 6010 m s^–1 and the speed of sound in air is 340 m s^–1. Calculate the angle between the normal at Q and the direction of the wave in air.

The wave is incident at point Q on the metal–air boundary. The wave makes an angle of 54° with the normal at Q. The speed of sound in the metal is 6010 m s^–1 and the speed of sound in air is 340 m s^–1. Calculate the angle between the normal at Q and the direction of the wave in air.

The wave is incident at point Q on the metal–air boundary. The wave makes an angle of 54° with the normal at Q. The speed of sound in the metal is 6010 m s^–1 and the speed of sound in air is 340 m s^–1. Calculate the angle between the normal at Q and the direction of the wave in air.

Friction and air resistance act on the bicycle and the girl when they move. Assume that all the energy is transferred from the battery to the electric motor. Determine the total average resistive force that acts on the bicycle and the girl.

Calculate the component of weight for the bicycle and girl acting down the slope.

The frequency of the sound wave in the metal is 250 Hz. Determine the wavelength of the wave in air.

The frequency of the sound wave in the metal is 250 Hz. Determine the wavelength of the wave in air.

The frequency of the sound wave in the metal is 250 Hz. Determine the wavelength of the wave in air.

Two blocks of masses m and 2m are travelling directly towards each other. Both are moving at the same constant speed v. The blocks collide and stick together.

What is the total momentum of the system before and after the collision?

Two blocks of masses m and 2m are travelling directly towards each other. Both are moving at the same constant speed v. The blocks collide and stick together.

What is the total momentum of the system before and after the collision?

Calculate the component of weight for the bicycle and girl acting down the slope.

The graph shows the variation with time of the resultant net force acting on an object. The object has a mass of 1kg and is initially at rest.

What is the velocity of the object at a time of 200 ms?

A. 8 m s^–1

B. 16 m s^–1

C. 8 km s^–1

D. 16 km s^–1

Calculate the component of weight for the bicycle and girl acting down the slope.

The battery continues to give an output power of 240 W. Assume that the resistive forces are the same as in (a)(iii).

Calculate the maximum speed of the bicycle and the girl up the slope.

Calculate the wavelength measured by the observer.

The graph shows the variation with time of the resultant net force acting on an object. The object has a mass of 1kg and is initially at rest.

What is the velocity of the object at a time of 200 ms?

A. 8 m s^–1

B. 16 m s^–1

C. 8 km s^–1

D. 16 km s^–1

A block is on the surface of a horizontal rotating disk. The block is at rest relative to the disk. The disk is rotating at constant angular velocity.

What is the correct arrow to represent the direction of the frictional force acting on the block at the instant shown?

A block is on the surface of a horizontal rotating disk. The block is at rest relative to the disk. The disk is rotating at constant angular velocity.

What is the correct arrow to represent the direction of the frictional force acting on the block at the instant shown?

The battery continues to give an output power of 240 W. Assume that the resistive forces are the same as in (a)(iii).

Calculate the maximum speed of the bicycle and the girl up the slope.

Determine the fundamental SI unit for k.

Calculate the wavelength measured by the observer.

Calculate the wavelength measured by the observer.

The battery continues to give an output power of 240 W. Assume that the resistive forces are the same as in (a)(iii).

Calculate the maximum speed of the bicycle and the girl up the slope.

Determine the fundamental SI unit for k.

Determine the fundamental SI unit for k.

The switch S is initially open. Calculate the total power dissipated in the circuit.

The switch S is initially open. Calculate the total power dissipated in the circuit.