A-LevelPhysicsGravitational fields9702/42 · May/June 2020 · Q110 Marks

An isolated solid sphere of radius r may be assumed to have its mass M concentrated at its centre. The magnitude of the gravitational potential at the surface of the sphere is φ. The sphere in (b) is a planet with radius r of 6.4 × 10⁶ m and mass M of 6.0 x 10²⁴ kg. The planet has no atmosphere. A rock of mass 3.4 x 10³ kg moves directly towards the planet. Its distance from the centre of the planet changes from 4r to 3r.

(a)Define gravitational potential at a point.[2]
(b)On Fig. 1.1, show the variation of the gravitational potential with distance d from the centre of the sphere for values of d from d = r to d = 4r. [Figure 1.1][3]
(c)(i)Calculate the change in gravitational potential energy of the rock.[3]
(c)(ii)Explain whether the rock's speed increases, decreases or stays the same.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[1] work done per unit mass
[1] (work done to) move mass from infinity (to the point)
[1] curve from r to 4r, with gradient of decreasing magnitude and starting at (r, ±ø)
[1] line passing through (2r, ±0.5φ) and (4r, ±0.25φ)
[1] line showing potential is negative throughout
[1] gravitational potential energy = (−) GMm / R
[1] change = (6.67 × 10–11 × 6.0 × 10²⁴ × 3.4 × 10³) / (6.4 × 10⁶) × [1/3 – 1/4]
[1] = 1.8 × 10¹⁰ J
[1] rock loses potential energy
[1] (so) kinetic energy increases so speed increases
[1] force is attractive
[1] moves towards planet so speeds up

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