State what is meant by gravitational field strength.

Show that V = –g(R + h).

Draw a graph, on the axes, to show the variation of the gravitational potential V of the planet with height h above the surface of the planet.

A planet has a radius of 3.1 × 10⁶ m. At a point P a distance 2.4 × 10⁷ m above the surface of the planet the gravitational field strength is 2.2 N kg^–1. Calculate the gravitational potential at point P, include an appropriate unit for your answer.

The diagram shows the path of an asteroid as it moves past the planet.

When the asteroid was far away from the planet it had negligible speed. Estimate the speed of the asteroid at point P as defined in (b).

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.

Show that the energy of photons from the UV lamp is about 10 eV.

Calculate, in J, the maximum kinetic energy of the emitted electrons.

Suggest, with reference to conservation of energy, how the variable voltage source can be used to stop all emitted electrons from reaching the collecting plate.

The variable voltage can be adjusted so that no electrons reach the collecting plate. Write down the minimum value of the voltage for which no electrons reach the collecting plate.

On the diagram, draw and label the equipotential lines at –0.4 V and –0.8 V.

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

Outline what is meant by electric potential at a point.

The electric potential at a point a distance 2.8 m from the centre of the sphere is 7.71 kV. Determine the radius of the sphere.

Comment on the angle at which the object meets equipotential surfaces around the sphere.

Show that the kinetic energy of the object is about 0.7 mJ.

Determine whether the object will reach the surface of the sphere.

Explain what is meant by the gravitational potential at the surface of a planet.

An unpowered projectile is fired vertically upwards into deep space from the surface of planet Venus. Assume that the gravitational effects of the Sun and the other planets are negligible.

The following data are available.

(i) Determine the initial kinetic energy of the projectile.

(ii) Describe the subsequent motion of the projectile until it is effectively beyond the gravitational field of Venus.

Outline why the gravitational potential is negative.

The gravitational potential due to the Sun at a distance r from its centre is V_S. Show that

rV_S = constant.

Calculate the gravitational potential energy of the Earth in its orbit around the Sun. Give your answer to an appropriate number of significant figures.

Calculate the total energy of the Earth in its orbit.

An asteroid strikes the Earth and causes the orbital speed of the Earth to suddenly decrease. Suggest the ways in which the orbit of the Earth will change.

Outline, in terms of the force acting on it, why the Earth remains in a circular orbit around the Sun.

Satellite X orbits 6600 km from the centre of the Earth.

Mass of the Earth = 6.0 x 10²⁴ kg

Show that the orbital speed of satellite X is about 8 km s^–1.

the orbital times for X and Y are different.

satellite Y requires a propulsion system.

The cable between the satellites cuts the magnetic field lines of the Earth at right angles.

Explain why satellite X becomes positively charged.

Satellite X must release ions into the space between the satellites. Explain why the current in the cable will become zero unless there is a method for transferring charge from X to Y.

The magnetic field strength of the Earth is 31 μT at the orbital radius of the satellites. The cable is 15 km in length. Calculate the emf induced in the cable.

Estimate the value of k in the following expression.

T = $2\pi \sqrt{\frac{m}{k}}$

Give an appropriate unit for your answer. Ignore the mass of the cable and any oscillation of satellite X.

Describe the energy changes in the satellite Y-cable system during one cycle of the oscillation.

Calculate, for the surface of $\text{Io}$, the gravitational field strength g_Io due to the mass of $\text{Io}$. State an appropriate unit for your answer.

Show that the $\frac{\mathrm{gravitational} \mathrm{potential} \mathrm{due} \mathrm{to} \mathrm{Jupiter} \mathrm{at} \mathrm{the} \mathrm{orbit} \mathrm{of} \mathrm{Io}}{ \mathrm{gravitational} \mathrm{potential} \mathrm{due} \mathrm{to} \mathrm{Io} \mathrm{at} \mathrm{the} \mathrm{surface} \mathrm{of} \mathrm{Io}}$ is about 80.

Outline, using (b)(i), why it is not correct to use the equation $\sqrt{\frac{2G\times \text{mass of Io}}{\text{radius of Io}}}$ to calculate the speed required for the spacecraft to reach infinity from the surface of $\text{Io}$.

An engineer needs to move a space probe of mass 3600 kg from Ganymede to Callisto. Calculate the energy required to move the probe from the orbital radius of Ganymede to the orbital radius of Callisto. Ignore the mass of the moons in your calculation. 

Explain why the electric potential decreases from A to B.

Draw, on the axes, the variation of electric potential $V$ with distance $r$ from the centre of the sphere.

Calculate the electric potential difference between points A and B.

Determine the charge $Q$ of the sphere.

The concept of potential is also used in the context of gravitational fields. Suggest why scientists developed a common terminology to describe different types of fields.

Outline how this diagram shows that the gravitational field strength of planet X decreases with distance from the surface.

The diagram shows part of the surface of planet X. The gravitational potential at the surface of planet X is –3V and the gravitational potential at point Y is –V.

Sketch on the grid the equipotential surface corresponding to a gravitational potential of –2V.

A meteorite, very far from planet X begins to fall to the surface with a negligibly small initial speed. The mass of planet X is 3.1 × 10²¹ kg and its radius is 1.2 × 10⁶ m. The planet has no atmosphere. Calculate the speed at which the meteorite will hit the surface.

At the instant of impact the meteorite which is made of ice has a temperature of 0 °C. Assume that all the kinetic energy at impact gets transferred into internal energy in the meteorite. Calculate the percentage of the meteorite’s mass that melts. The specific latent heat of fusion of ice is 3.3 × 10⁵ J kg^–1.

Show that the intensity of the solar radiation at the location of Titan is 16 W m⁻².

Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the average intensity of solar radiation absorbed by the whole surface of Titan is 3.1 W m⁻².

Show that the equilibrium surface temperature of Titan is about 90 K.

The mass of Titan is 0.025 times the mass of the Earth and its radius is 0.404 times the radius of the Earth. The escape speed from Earth is 11.2 km s⁻¹. Show that the escape speed from Titan is 2.8 km s⁻¹.

The orbital radius of Titan around Saturn is $R$ and the period of revolution is $T$.

Show that $T^2=\frac{4{\mathrm{\pi }}^2{R}^{ 3}}{GM}$ where $M$ is the mass of Saturn.

The orbital radius of Titan around Saturn is 1.2 × 10⁹m and the orbital period is 15.9 days. Estimate the mass of Saturn.

Show that the mass of a nitrogen molecule is 4.7 × 10⁻²⁶ kg.

Estimate the root mean square speed of nitrogen molecules in the Titan atmosphere. Assume an atmosphere temperature of 90 K.

Discuss, by reference to the answer in (b), whether it is likely that Titan will lose its atmosphere of nitrogen.

The charge per unit area on the surface of the wall is σ. It can be shown that the electric field strength E due to the charge on the wall is given by the equation

$E=\frac{\sigma }{2{\epsilon }_0}$.

Demonstrate that the units of the quantities in this equation are consistent.

The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.

Determine the horizontal force that acts on the ball.

The charge on the ball is 1.2 × 10⁻⁶C. Determine σ.

The thread breaks. Explain the initial subsequent motion of the ball.

Calculate the charge on Q. State your answer to an appropriate number of significant figures.

Outline, without calculation, whether or not the electric potential at P is zero.

Show that the charge on the surface of the sphere is +18 μC.

Describe, in terms of electron flow, how the smaller sphere becomes charged.

Predict the charge on each sphere.

Show that the total energy of the planet is given by the equation shown.

$E=\frac{1}{2}mV$

Suppose the star could contract to half its original radius without any loss of mass. Discuss the effect, if any, this has on the total energy of the planet.

The diagram shows some of the electric field lines for two fixed, charged particles X and Y.

The magnitude of the charge on X is $Q$ and that on Y is $q$. The distance between X and Y is 0.600 m. The distance between P and Y is 0.820 m.

At P the electric field is zero. Determine, to one significant figure, the ratio $\frac{Q}{q}$.

State how the density of a nucleus varies with the number of nucleons in the nucleus.

Show that the nuclear radius of phosphorus-31 (${}_{15}^{31}\text{P}$) is about 4 fm.

State the maximum distance between the centres of the nuclei for which the production of ${}_{15}^{32}\text{P}$ is likely to occur.

Determine, in J, the minimum initial kinetic energy that the deuterium nucleus must have in order to produce ${}_{15}^{32}\text{P}$. Assume that the phosphorus nucleus is stationary throughout the interaction and that only electrostatic forces act.

${}_{15}^{32}\text{P}$ 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.

State what is meant by decay constant.

In a fresh pure sample of ${}_{15}^{32}\text{P}$ the activity of the sample is 24 Bq. After one week the activity has become 17 Bq. Calculate, in s^–1, the decay constant of ${}_{15}^{32}\text{P}$.

Show that the speed $v$ of the electron with mass $m$, is given by $v=\sqrt{\frac{2k{e}^2}{mr}}$.

Hence, deduce that the total energy of the electron is given by $E_{\mathrm{TOT}}=-\frac{k{e}^2}{r}$.

In this model the electron loses energy by emitting electromagnetic waves. Describe the predicted effect of this emission on the orbital radius of the electron.

Show that the de Broglie wavelength $\lambda$ of the electron in the $n=3$ state is  $\lambda =5.1\times {10}^{-10}$ m.

The formula for the de Broglie wavelength of a particle is $\lambda =\frac{h}{mv}$.

Estimate for $n=3$, the ratio $\frac{\mathrm{circumference} \mathrm{of} \mathrm{orbit}}{\mathrm{de} \mathrm{Broglie} \mathrm{wavelength} \mathrm{of} \mathrm{electron}}$.

State your answer to one significant figure.

The description of the electron is different in the Schrodinger theory than in the Bohr model. Compare and contrast the description of the electron according to the Bohr model and to the Schrodinger theory.

Calculate the total length of aluminium foil that the student will require.

The plastic film begins to conduct when the electric field strength in it exceeds 1.5 MN C^–1. Calculate the maximum charge that can be stored on the capacitor.

The resistor R in the circuit has a resistance of 1.2 kΩ. Calculate the time taken for the charge on the capacitor to fall to 50 % of its fully charged value.

The ammeter is replaced by a coil. Explain why there will be an induced emf in the coil while the capacitor is discharging.

Suggest one change to the discharge circuit, apart from changes to the coil, that will increase the maximum induced emf in the coil.

Outline the origin of the force that acts on Phobos.

Outline why this force does no work on Phobos.

The orbital period T of a moon orbiting a planet of mass M is given by

$$\frac{R^3}{T^2}=kM$$

where R is the average distance between the centre of the planet and the centre of the moon.

Show that $k=\frac{G}{4{\pi }^2}$

The following data for the Mars–Phobos system and the Earth–Moon system are available:

Mass of Earth = 5.97 × 10²⁴ kg

The Earth–Moon distance is 41 times the Mars–Phobos distance.

The orbital period of the Moon is 86 times the orbital period of Phobos.

Calculate, in kg, the mass of Mars.

The graph shows the variation of the gravitational potential between the Earth and Moon with distance from the centre of the Earth. The distance from the Earth is expressed as a fraction of the total distance between the centre of the Earth and the centre of the Moon.

Determine, using the graph, the mass of the Moon.

Explain why a centripetal force is needed for the planet to be in a circular orbit.

Calculate the value of the centripetal force.

Show that the gravitational potential due to the planet and the star at the surface of the planet is about −5 × 10⁹J kg⁻¹.

Estimate the escape speed of the spacecraft from the planet–star system.

Calculate the electric potential at O.

Sketch, on the axes, the variation of the electric potential V with distance between X and Y.

Identify the direction of the resultant force acting on Z as it oscillates.

Deduce whether the motion of Z is simple harmonic.