Gravitational fields and Newton's law of gravitationEdexcel International A Level Physics: Subtopic test

1. 1
   Treat the Earth as a uniform sphere of mass 5.97 × 10²⁴ kg and radius 6.37 × 10⁶ m. A communications satellite of mass 450 kg is 3.59 × 10⁷ m above the Earth's surface. The gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².

   (a)

   What is the gravitational field strength of the Earth at the satellite?

   [1 mark]

   • A0.31 N kg⁻¹
   • B0.22 N kg⁻¹
   • C9.81 N kg⁻¹
   • D9.4 × 10⁶ N kg⁻¹

   (b)

   What is the gravitational force on the satellite due to the Earth?

   [1 mark]

   • A4.4 × 10³ N
   • B1.4 × 10² N
   • C1.0 × 10² N
   • D5.0 × 10⁻⁴ N

   (c)

   Calculate the gravitational potential at the position of the satellite.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The Earth has mass 5.97 × 10²⁴ kg and the Moon has mass 7.35 × 10²² kg. The distance between their centres is 3.84 × 10⁸ m. Treat both as point masses at their centres. G = 6.67 × 10⁻¹¹ N m² kg⁻².

   (a)

   What is the gravitational force between the Earth and the Moon?

   [1 mark]

   • A7.6 × 10²⁸ N
   • B3.0 × 10³⁰ N
   • C1.0 × 10²⁰ N
   • D2.0 × 10²⁰ N

   (b)

   At what distance from the centre of the Earth, along the line joining the centres, is the resultant gravitational field strength due to the Earth and the Moon zero?

   [1 mark]

   • A3.46 × 10⁸ m
   • B1.92 × 10⁸ m
   • C3.80 × 10⁸ m
   • D3.8 × 10⁷ m

   (c)

   Calculate the gravitational field strength of the Moon at the centre of the Earth, and state its direction.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In a hydrogen atom an electron and a proton are separated by 5.3 × 10⁻¹¹ m. The electron has mass 9.11 × 10⁻³¹ kg and the proton has mass 1.67 × 10⁻²⁷ kg. Each has a charge of magnitude 1.60 × 10⁻¹⁹ C. G = 6.67 × 10⁻¹¹ N m² kg⁻² and the constant in Coulomb's law, k = 1/(4πε₀), is 8.99 × 10⁹ N m² C⁻².

   (a)

   Calculate the gravitational force between the electron and the proton.

   [3 marks]

   (b)

   Calculate the electric force between the electron and the proton, and use it to deduce how many times larger it is than the gravitational force. State one similarity between the two types of force.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Physicists describe the gravitational field of a point mass using ideas that are very similar to those used for the electric field of a point charge. The Moon has mass 7.35 × 10²² kg and radius 1.74 × 10⁶ m, and can be treated as a uniform sphere, so its field outside it is the same as that of a point mass at its centre. G = 6.67 × 10⁻¹¹ N m² kg⁻².

   (a)

   Compare the gravitational field of a point mass with the electric field of a point charge.

   [6 marks]

   (b)

   Derive the equation g = GM/r² for the gravitational field strength at a distance r from the centre of a point mass M. Hence calculate the weight of an 85 kg astronaut on the surface of the Moon.

   [6 marks]

   Total for question 4: 12 marks

End of questions