Gravitational field strengthAQA A-Level Physics: Subtopic test

1. 1
   A Mars lander team models Mars as a uniform sphere of mass 6.42 × 10²³ kg and radius 3.39 × 10⁶ m. A small test mass is released at the surface of the planet.

   (a)

   Which statement defines gravitational field strength at a point?

   [1 mark]

   • AThe work done per unit mass in bringing a small mass from infinity to the point
   • BThe mass of the planet per unit volume
   • CThe gravitational force acting per unit mass on a small test mass placed at the point
   • DThe gravitational force between two bodies each of mass 1 kg

   (b)

   Which is an acceptable SI unit for gravitational field strength?

   [1 mark]

   • AN kg
   • BN kg⁻¹
   • CN m² kg⁻²
   • Dkg m⁻¹

   (c)

   Calculate the gravitational field strength at the surface of Mars. Use $G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The gravitational field around an isolated, uniform planet is represented by gravitational field lines drawn in the space outside the planet.

   (a)

   Which description of the field lines outside the planet is correct?

   [1 mark]

   • AParallel lines directed away from the planet
   • BClosed circular loops around the planet
   • CRadial lines directed away from the centre of the planet
   • DRadial lines directed towards the centre of the planet

   (b)

   The field lines are closer together near the surface of the planet than far away from it. What does this show?

   [1 mark]

   • AThe gravitational field strength is greater near the surface
   • BThe gravitational field strength is smaller near the surface
   • CThe planet has a smaller mass near the surface
   • DThe field is uniform

   (c)

   Explain why the gravitational field near the surface of the planet can be treated as uniform over a height of a few metres, but not over a height of several thousand kilometres.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The International Space Station orbits the Earth at a height of 400 km above the surface. The Earth may be treated as a uniform sphere of mass 5.97 × 10²⁴ kg and radius 6.37 × 10⁶ m.

   (a)

   Calculate the gravitational field strength at the height of the space station. Use $G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$.

   [3 marks]

   (b)

   Compare this value with the field strength at the Earth's surface, and explain why astronauts on the station feel weightless even though the field strength there is almost as large as at the surface.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Astronomers discover a rocky exoplanet with a mass 4.0 times the mass of the Earth and a radius 1.6 times the radius of the Earth. Take the Earth's surface gravitational field strength as 9.81 N kg⁻¹. For part (b), use data for the Earth–Moon system: Earth mass 5.97 × 10²⁴ kg, Moon mass 7.35 × 10²² kg, centre-to-centre distance 3.84 × 10⁸ m.

   (a)

   Calculate the gravitational field strength at the surface of the exoplanet and the weight of a 70 kg astronaut standing on it. Compare the astronaut's weight with that on Earth.

   [6 marks]

   (b)

   A spacecraft travels along the line from the Earth to the Moon. Determine the distance from the centre of the Earth at which the resultant gravitational field strength due to the Earth and the Moon is zero, and explain why this point lies much closer to the Moon than to the Earth.

   [6 marks]

   Total for question 4: 12 marks

End of questions