Charon is a moon of Pluto that has a mass equal to 1/9 that of Pluto.

Charon is a moon of Pluto that has a mass equal to d that of Pluto.

X is the point at which the resultant gravitational field due to Pluto and Charon is zero.

What is the distance of X from the centre of Pluto?

The distance between the centres of the Earth and the Moon is 3.8 × 10⁸ m. The mass of the Earth is 6.0 × 10²⁴ kg and the mass of the Moon is 7.4 × 10²² kg.

A spacecraft of mass 10 × 10³ kg is moving along a line joining their centres.

At what distance from the centre of the Earth would the spacecraft experience no resultant force due to the Earth and the Moon?

Which of the following statements about Newton’s law of gravitation is correct?

Newton’s gravitational law explains

Two planets X and Y are in concentric circular orbits about a star S. The radius of the orbit of X is R and the radius of orbit of Y is 2R .

The gravitational force between X and Y is F when angle SXY is 90°, as shown in the diagram.

What is the gravitational force between X and Y when they are nearest to each other?

The gravitational constant, G, is a constant of proportionality in Newton’s law of gravitation. The permittivity of free space, ε₀, is a constant of proportionality in Coulomb’s law.

When comparing the electrostatic force acting on a pair of charged particles to the gravitational force between them, the product ε₀G can appear in the calculation.

Which is a unit for ε₀G?

A spacecraft of mass m is at the mid-point between the centres of a planet of mass M₁ and its moon of mass M₂. If the distance between the spacecraft and the centre of the planet is d, what is the magnitude of the resultant gravitational force on the spacecraft?

When a space shuttle is in a low orbit around the Earth it experiences gravitational forces F_E due to the Earth, F_M due to the Moon and F_S due to the Sun. Which one of the following correctly shows how the magnitudes of these forces are related to each other?

mass of Sun = 1.99 × 10³⁰ kg

mass of Moon = 7.35 × 10²² kg

mean distance from Earth to Sun = 1.50 × 10¹¹ m

mean distance from Earth to Moon = 3.84 × 10⁸ m

Which one of the following gives a correct unit for

An object on the surface of a planet of radius R and mass M has weight W.

What would be the weight of the same object when on the surface of a planet of radius 2R and mass 2M?

Which one of the following statements about Newton’s law of gravitation is correct?

Newton’s law of gravitation explains

If an electron and proton are separated by a distance of 5 × 10^–11 m, what is the approximate gravitational force of attraction between them?

Masses of M and 2M exert a gravitational force F on each other when the distance between their centres is r. What is the gravitational force between masses of 2M and 4M when the distance between their centres is 4r?

At the surface of the Earth the gravitational field strength is g, and the gravitational potential is V. The radius of the Earth is R. An object, whose weight on the surface of the Earth is W, is moved to a height 3R above the surface. Which line, A to D, in the table gives the weight of the object and the gravitational potential at this height?

The gravitational force between two uniform spheres is 3.1 × 10^–9 N when the distance between their centres is 150 mm. If the mass of one sphere is 2.5 kg, what is the mass of the other?

Two protons are 1.0 × 10^–14 m apart. Approximately how many times is the electrostatic force between them greater than the gravitational force between them?

(Use the Data and Formulae booklet)

A projectile moves in a gravitational field. Which one of the following is a correct statement about the gravitational force acting on the projectile?

Two identical spheres exert a gravitational force F on each other. What is the gravitational force between two spheres, each twice the mass of one of the original spheres, when the separation of their centres is twice the original separation?

Which one of the following graphs correctly shows the relationship between the gravitational force, F, between two masses and their separation r.

A projectile moves in a gravitational field. Which one of the following is a correct statement for the gravitational force acting on the projectile?

Two protons, each of mass m and charge e, are a distance d apart. Which one of the following expressions correctly gives the ratio shown for the forces acting between them?

Two identical conducting spheres on insulating supports carry charges of magnitude Q and 2Q respectively. When separated by distance d, the electrostatic repulsive force is F. The spheres are made to touch and then restored to their original separation d. If there is no loss of charge what is the new force of repulsion?

When two similar spherical objects of radius R are touching, the gravitational force of attraction between them is F. When the gravitational force between them is F/4, the distance between the surfaces of the spheres is

The Earth can be assumed to be a uniform sphere of radius R. What is the mean density of the Earth?

The distance between the Sun and Mars varies from 2.1 × 10¹¹ m to 2.5 × 10¹¹ m. When Mars is closest to the Sun, the force of gravitational attraction between them is F. What is the force of gravitational attraction between them when they are furthest apart?

An electron on the surface of the Earth is placed in an electric field of strength 5000 N C⁻¹. What is (electrical force/gravitational force) for the electron?

A planet has a radius half the Earth’s radius and a mass a quarter of the Earth’s mass. What is the approximate gravitational field strength on the surface of the planet?

Two stars of mass M and 4M are at a distance d between their centres.

The resultant gravitational field strength is zero along the line between their centres at a distance y from the centre of the star of mass M.

What is the value of the ratio y/d ?

Two identical uniform spheres each of radius R are placed in contact. The gravitational force between them is F.

The spheres are now separated until the force of attraction is F/9.

What is the distance between the surfaces of the spheres after they have been separated?

A satellite of mass m is in a circular orbit at height R above the surface of a uniform spherical planet of radius R and density ρ. What is the force of gravitational attraction between the satellite and the planet?

The following data refers to two planets, P and Q.

The gravitational field strength at the surface of P is 13.4 N kg^–1.

What is the gravitational field strength at the surface of Q?

The diagram shows an isolated binary star system. The two stars have equal masses, M, and the distance between their centres is r. The point P is half-way between the two stars. What is the gravitational field strength at P?

In the equation below, X represents a physical variable in an electric or a gravitational field, a is a constant, b is either mass or charge and n is a number.

The gravitational field strengths at the surfaces of the Earth and the Moon are 9.8 N kg^–1 and 1.7 N kg^–1 respectively. If the mass of the Earth is 81 × the mass of the Moon, what is the ratio of the radius of the Earth to the radius of the Moon?

A small mass is situated at a point on a line joining two large masses m1 and m2 such that it experiences no resultant gravitational force. Its distance from the centre of mass of m1 is r1 and its distance from the centre of mass of m2 is r2. What is the value of the ratio $$\frac{r_1}{r_2}$$

Which one of the following gives a correct unit for $$\left(\frac{g^2}{G}\right)$$

The gravitational field strength at the surface of the Earth is 6 times its value at the surface of the Moon. The mean density of the Moon is 0.6 times the mean density of the Earth.

What is the value of the ratio (radius of the Earth / radius of the Moon)?

Which one of the following statements about gravitational fields is incorrect?

The gravitational field strength on the surface of a planet orbiting a star is 8.0 N kg^–1. If the planet and star have a similar density but the diameter of the star is 100 times greater than the planet, what would be the gravitational field strength at the surface of the star?

A spherical planet of uniform density ρ has radius R.

Which line, A to D, in the table gives correct expressions for the mass of the planet and the gravitational field strength at its surface?

A planet has a radius half the Earth’s radius and a mass a quarter of the Earth’s mass. What is the approximate gravitational field strength on the surface of the planet?

The diagram shows two point masses each of mass m separated by a distance 2r.

What is the value of the gravitational field strength at the mid-point, P, between the two masses?

What would the period of rotation of the Earth need to be if objects at the equator were to appear weightless?

radius of Earth = 6.4 × 10⁶ m

The gravitational potential difference between the surface of a planet and a point P, 10 m above the surface, is 8.0 J kg^–1. Assuming a uniform field, what is the value of the gravitational field strength in the region between the planet’s surface and P?

The radius of a certain planet is x times the radius of the Earth and its surface gravitational field strength is y times that of the Earth.

Which one of the following gives the ratio (mass of the planet / mass of the Earth)?

When at the surface of the Earth, a satellite has weight W and gravitational potential energy –U. It is projected into a circular orbit whose radius is equal to twice the radius of the Earth. Which line, A to D, in the table shows correctly what happens to the weight of the satellite and to its gravitational potential energy?

A projectile moves in a gravitational field. Which one of the following is a correct statement for the gravitational force acting on the projectile?

The Earth has density ρ and radius R. The gravitational field strength at the surface is g. What is the gravitational field strength at the surface of a planet of density 2ρ and radius 2R?

The following data refer to two planets.

The gravitational field strength at the surface of P is 13.4 N kg^–1. What is the gravitational field strength at the surface of Q?

A planet has a radius half of the Earth’s radius and a mass a quarter of the Earth’s mass. What is the approximate gravitational field strength on the surface of the planet?

At a distance R from a fixed charge, the electric field strength is E and the electric potential is V. Which line, A to D, gives the electric field strength and electric potential at a distance 2R from the charge?

A planet of mass M and radius R rotates so rapidly that loose material at the equator just remains on the surface. What is the period of rotation of the planet?

G is the universal gravitational constant.

Which one of the following has different units to the other three?

The gravitational potential difference between the surface of a planet and a point P, 10 m above the surface, is 8.0 J kg^{− 1} . Assuming a uniform field, what is the value of the gravitational field strength in the region between the planet’s surface and P?

For which of the following relationships is the quantity y related to the quantity x by the relationship shown

Graph 1 shows the variation of electric field strength E with separation r for two point charges.

Graph 2 shows the corresponding variation of electric potential V with separation.

Which line correctly relates data for the two graphs?

The graph shows how the gravitational potential varies with distance between two planets, K and L, that have the same radius.

Which statement is correct?

The diagram shows equipotential lines near a group of asteroids. Which arrow shows the direction of the gravitational field at X?

Planet N has a gravitational potential –V at its surface. Planet M has double the density and double the radius of planet N. Both planets are spherical and have uniform density.

What is the gravitational potential at the surface of planet M?

The radius of a planet is R. The gravitational potential at the surface of the planet due to its mass is −4000 J kg⁻¹.

What is the gravitational potential at a distance 2R from the centre of the planet?

X and Y are two stars of equal mass M. The distance between their centres is d.

What is the gravitational potential at the mid-point P between them?

Which one of the following statements about gravitational potential is incorrect?

Which one of the following statements about gravitational potential is correct?

A uniform electric field of electric field strength E is aligned so it is vertical. An ion moves vertically through a small distance Δd from point X to point Y in the field.There is a uniform gravitational field of field strength g throughout the region.

Which line, A to D, in the table correctly gives the gravitational potential difference, and the electric potential difference, between X and Y?

Mars has a diameter approximately 0.5 that of the Earth, and a mass of 0.1 that of the Earth.

The gravitational potential at the Earth’s surface is −63 MJ kg^–1.

What is the approximate value of the gravitational potential at the surface of Mars?

The diagram shows two points, P and Q, at distances r and 2r from the centre of a planet. The gravitational potential at P is −16 kJ kg⁻¹. What is the work done on a 10 kg mass when it is taken from P to Q?

When a charge moves between two points in an electric field, or a mass moves between two points in a gravitational field, energy may be transferred.

Which one of the following statements is correct?

Which one of the following statements about gravitational fields is incorrect?

The gravitational potential at the surface of the Earth, of radius R, is V. What is the gravitational potential at a point at a height R above the Earth’s surface?

A 10 μF capacitor is fully charged to a pd of 3.0 kV. The energy stored in the capacitor can be used to lift a load of 5.0 kg through a vertical height h. What is the approximate value of h?

At the surface of the Earth the gravitational field strength is g, and the gravitational potential is V. The radius of the Earth is R. An object, whose weight on the surface of the Earth is W, is moved to a height 3R above the surface. Which line, A to D, in the table gives the weight of the object and the gravitational potential at this height?

The diagram shows two positions, X and Y, on the Earth’s surface. Which line, A to D, in the table gives correct comparisons at X and Y for gravitational potential and angular velocity?

A 10 mF capacitor is charged to 10 V and then discharged completely through a small motor. During the process, the motor lifts a weight of mass 0.10 kg. If 10% of the energy stored in the capacitor is used to lift the weight, through what approximate height will the weight be lifted?

Which one of the following could be a unit of gravitational potential?

When at the surface of the Earth, a satellite has weight W and gravitational potential energy –U. It is projected into a circular orbit whose radius is equal to twice the radius of the Earth. Which line, A to D, in the table shows correctly what happens to the weight of the satellite and to its gravitational potential energy?

Two protons are 1.0 × 10^–14 m apart. Approximately how many times is the electrostatic force between them greater than the gravitational force between them?

The graph shows how the gravitational potential, V, varies with the distance, r , from the centre of the Earth.

What does the gradient of the graph at any point represent?

Near the surface of a planet the gravitational field is uniform and for two points, 10 m apart vertically, the gravitational potential difference is 3 J kg^–1. How much work must be done in raising a mass of 4 kg vertically through 5 m?

At a distance R from a fixed charge, the electric field strength is E and the electric potential is V. Which line, A to D, gives the electric field strength and electric potential at a distance 2R from the charge?

Which one of the following has different units to the other three?

The gravitational potential difference between the surface of a planet and a point P, 10 m above the surface, is 8.0 J kg^{− 1} . Assuming a uniform field, what is the value of the gravitational field strength in the region between the planet’s surface and P?

A mass of 5 kg is moved in a gravitational field from a point X at which the gravitational potential is –20 J kg^–1 to a point Y where it is –10 J kg^–1. The change in potential energy of the mass, in J, between X and Y is

Graph 1 shows the variation of electric field strength E with separation r for two point charges.

Graph 2 shows the corresponding variation of electric potential V with separation.

Which line in the table correctly relates data for the two graphs?

g is the strength of the gravitational field at the surface of the Earth; R is the radius of the Earth. The potential energy lost by a satellite of mass m falling to the Earth’s surface from a height R above the surface is

A spacecraft of mass 1.0 × 10⁶ kg is in orbit around the Sun at a radius of 1.1 × 10¹¹ m

The spacecraft moves into a new orbit of radius 2.5 × 10¹¹ m around the Sun.

What is the total change in gravitational potential energy of the spacecraft?

Which graph shows the relationship between the time period T and the orbital radius r of a planet in orbit around the Sun?

A satellite X of mass m is in a concentric circular orbit of radius R about a planet of mass M.

What is the kinetic energy of X?

Satellites X and Y orbit the Earth at distances R and 4R respectively, as shown in the diagram.

Which statement is incorrect?

A geosynchronous satellite is in a constant radius orbit around the Earth. The Earth has a mass of 6.0 × 10²⁴ kg and a radius of 6.4 × 10⁶ m.

What is the height of the satellite above the Earth’s surface?

A satellite X is in a circular orbit of radius r about the centre of a spherical planet of mass M. Which line, A to D, in the table gives correct expressions for the centripetal acceleration a and the speed v of the satellite?

A satellite orbiting the Earth moves to an orbit which is closer to the Earth.

Which line shows correctly what happens to the speed of the satellite and to the time it takes for one orbit of the Earth?

Two satellites P and Q, of equal mass, orbit the Earth at radii R and 2R respectively. Which one of the following statements is correct?

The Earth moves around the Sun in a circular orbit with a radius of 1.5 × 10⁸ km. What is the Earth’s approximate speed?

Two satellites, P and Q, of the same mass, are in circular orbits around the Earth. The radius of the orbit of Q is three times that of P. Which one of the following statements is correct?

A satellite is in orbit at a height h above the surface of a planet of mass M and radius R.

What is the velocity of the satellite?

A satellite of mass m travels in a circular orbit of radius r around a planet of mass M. Which one of the following expressions gives the angular speed of the satellite?

As a comet orbits the Sun the distance between the comet and the Sun continually changes. As the comet moves towards the Sun this distance reaches a minimum value. Which one of the following statements is incorrect as the comet approaches this minimum distance?

An artificial satellite of mass m is in a stable circular orbit of radius r around a planet of mass M. Which one of the following expressions gives the speed of the satellite? G is the universal gravitational constant.

A planet of mass M and radius R rotates so rapidly that loose material at the equator only just remains on the surface. What is the period of rotation of the planet?

G is the universal gravitational constant.

What is the angular speed of a satellite in a geo-synchronous orbit around the Earth?

A satellite is in orbit at a height h above the surface of a planet of mass M and radius R. What is the velocity of the satellite?

Satellites N and F have the same mass and move in circular orbits about the same planet. N is the nearer satellite and F is the more distant. Which one of the following is smaller for N than for F?