A-LevelPhysicsGravitational fields9702/43 · Oct/Nov 2018 · Q17 Marks

State what is meant by gravitational potential at a point.

(a)(i)State what is meant by gravitational potential at a point.[2]
(a)(ii)Suggest why, for small changes in height near the Earth's surface, gravitational potential is approximately constant.[2]
(b)The Moon may be considered to be a uniform sphere with a diameter of 3.5 × 10³ km and a mass of 7.4 x 10²² kg. A meteor strikes the Moon and, during the collision, a rock is sent off from the surface of the Moon with an initial speed v. Assuming that the Moon is isolated in space, determine the minimum speed of the rock such that it does not return to the Moon's surface. Explain your working. minimum speed = .............................................. ms⁻¹ [3][3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

[B1] work done per unit mass
[B1] work done moving mass from infinity (to the point)
[B1] (near Earth's surface change in) height << radius or height much less than radius
[B1] potential inversely proportional to radius and radius approximately constant (so potential approximately constant)
[B1] initial kinetic energy = (-) potential energy (at surface)
[C1] or 1/2mv² = GMm/r
[C1] v² = (2 × 6.67 × 10⁻¹¹ × 7.4 × 10²²)/(0.5 × 3.5 × 10⁶)
[A1] v = 2.4 × 10³ ms⁻¹

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