A-LevelPhysicsGravitational fields9702/41 · Oct/Nov 2021 · Q29 Marks
Define gravitational potential.
- (a)Define gravitational potential.[2]
- (b)(i)The Earth E and the Moon M can both be considered as isolated point masses at their centres. The mass of the Earth is 5.98 × 10²⁴ kg and the mass of the Moon is 7.35 x 10²² kg. The Earth and the Moon are separated by a distance of 3.84 x 10⁸ m, as shown in [Figure 2.1]. P is a point, on the line joining the centres of E and M, where the resultant gravitational field strength is zero. Point P is at a distance x from the centre of the Earth. Explain how it is possible for the gravitational field strength to be zero despite the presence of two large masses nearby.[2]
- (b)(ii)Show that x is approximately 3.5 x 10⁸ m.[2]
- (b)(iii)Calculate the gravitational potential φ at point P.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [B1] work done per unit mass
- [B1] (work done in) moving mass from infinity
- [B1] (gravitational) fields from the Earth and Moon are in opposite directions
- [B1] (resultant is zero where gravitational) fields are equal (in magnitude)
- [C1] g ∝ M/r²
- [A1] leading to x = 3.5 × 10⁸ (m)
- [C1] φ (Earth) = (−)6.67 × 10⁻¹¹ × (5.98 × 10²⁴ / 3.5 × 10⁸)
- [C1] and φ (Moon) = (−)6.67 × 10⁻¹¹ × (7.35 × 10²² / 0.38 × 10⁸)
- [A1] = – 1.3 × 10⁸ J kg⁻¹
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