Gravitational potentialAQA A-Level Physics: Subtopic test

1. 1
   A space agency is planning to lift a probe of mass 1200 kg away from the Earth. Treat the Earth as a uniform sphere of mass 5.97 × 10²⁴ kg and radius 6.37 × 10⁶ m.

   (a)

   The gravitational potential at the Earth's surface is negative. Which statement gives the reason?

   [1 mark]

   • AThe gravitational force on the probe is repulsive
   • BThe gravitational field strength is negative at the surface
   • CThe mass of the Earth is negative in the equation for potential
   • DThe potential is defined as zero at infinity and the field is attractive, so work must be done on the probe to take it to infinity

   (b)

   Which value is the gravitational potential at the Earth's surface? Use $G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$.

   [1 mark]

   • A−6.25 × 10⁷ J kg⁻¹
   • B+6.25 × 10⁷ J kg⁻¹
   • C−9.81 J kg⁻¹
   • D−3.98 × 10¹⁴ J kg⁻¹

   (c)

   The probe is moved between two points in the Earth's field, where the potentials are −6.25 × 10⁷ J kg⁻¹ and −5.80 × 10⁷ J kg⁻¹. Calculate the work that must be done on the probe by an external force.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student studies the equipotential surfaces around an isolated, uniform planet and considers the work done when a small mass is moved between points in the field.

   (a)

   A small mass is moved between two points on the same equipotential surface. What is the work done by the gravitational field on the mass?

   [1 mark]

   • AIt is positive, because the mass moves closer to the planet
   • BIt is zero
   • CIt is negative, because the mass moves further from the planet
   • DIt depends on the path taken between the points

   (b)

   Which statement correctly describes the equipotential surfaces around the planet?

   [1 mark]

   • AParallel planes at right angles to the surface
   • BCircles lying in a single plane through the planet
   • CConcentric spheres, perpendicular to the field lines
   • DSpheres whose radius is proportional to the potential

   (c)

   Explain why no work is done on a small mass when it is moved along an equipotential surface.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Between distances r = 7.0 × 10⁶ m and r = 9.0 × 10⁶ m from the centre of the Earth, a graph of gravitational field strength g against r is approximately a straight line, falling from 8.1 N kg⁻¹ to 4.9 N kg⁻¹. The Earth has mass 5.97 × 10²⁴ kg.

   (a)

   Use the graph information to estimate the change in gravitational potential between these two distances.

   [3 marks]

   (b)

   Calculate the change in potential between these distances using $V = -GM/r$, and explain why it differs from your estimate in (a). Use $G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The Moon has mass 7.35 × 10²² kg and radius 1.74 × 10⁶ m. A lunar mission plans to lift a 250 kg instrument module from the Moon's surface to a point 1.00 × 10⁶ m above the surface. Treat the Moon as a uniform sphere.

   (a)

   Calculate the work that must be done to lift the module to this height. Use $G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$.

   [6 marks]

   (b)

   Describe how the gravitational potential V and the gravitational field strength g vary with distance r outside the Moon, and explain how g is related to the graph of V against r and V is related to the graph of g against r.

   [6 marks]

   Total for question 4: 12 marks

End of questions