CourseCourseConceptConcept

CAIE A-Level Physics A2 13.4.2 Gm R for the Gravitational Potential in the Field Due to a Point Mass Questions

Practise using φ = −GM/r to calculate signed gravitational potentials, compare distances, sketch inverse-distance graphs and combine point-mass contributions.

Syllabus
2028–2030
Course
Physics 9702
Level
A2

Exam points

  • Calculate a surface gravitational potential with φ = −GM/r, retaining the negative sign and J kg⁻¹ units.
  • Use the inverse-distance relationship to express one potential as a multiple of another.
  • Rearrange φ = −GM/r to determine the source mass from a potential and centre distance.
  • Represent the negative inverse-distance variation with a curved graph and correctly scaled points.
  • Add the signed potentials due to separate point masses at the same point.
  • Calculate a potential difference using the distances from the source centre at both positions.
  • Explain why potential changes little when a height change is much smaller than the source radius.

CAIE A-Level Physics A2 13.4.2 Gm R for the Gravitational Potential in the Field Due to a Point Mass Questions question 1

[Maximum number: 3]

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 kg5.98 \times 10^{24} \mathrm{~kg} and the mass of the Moon is 7.35×1022 kg7.35 \times 10^{22} \mathrm{~kg}. The Earth and the Moon are separated by a distance of 3.84×108 m3.84 \times 10^{8} \mathrm{~m}, as shown in Fig. 2.1.

Fig. 2.1 (not to scale)

Fig. 2.1 (not to scale)

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.

Calculate the gravitational potential ϕ\phi at point P .

ϕ=………………………………………...Jkg−1[3]\phi=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . . \mathrm{Jkg}^{-1}[3]
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