Force fields and Newton's law of gravitationAQA A-Level Physics: Subtopic test

1. 1
   A torsion-balance experiment measures the gravitational attraction between a large lead sphere of mass 15 kg and a small lead sphere of mass 0.015 kg. The centres of the spheres are 0.060 m apart and the spheres are uncharged.

   (a)

   Which statement about the gravitational forces between the two spheres is correct?

   [1 mark]

   • AThe force on the large sphere is greater than the force on the small sphere
   • BThe forces on the two spheres are equal in magnitude and each sphere is attracted towards the other
   • CThe force on the small sphere is repulsive because the spheres are uncharged
   • DNo force acts unless the two spheres are touching

   (b)

   The small sphere is moved so that the separation of the centres is doubled to 0.120 m. What happens to the gravitational force between the spheres?

   [1 mark]

   • AIt halves
   • BIt doubles
   • CIt falls to one quarter of its original value
   • DIt falls to one eighth of its original value

   (c)

   Calculate the magnitude of the gravitational force on the small sphere. Use $G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student compares the gravitational field around a planet with the electric field around an isolated, positively charged metal sphere. Both bodies are treated as point sources.

   (a)

   Which statement describes a similarity between the gravitational field of the planet and the electric field of the sphere?

   [1 mark]

   • ABoth forces on a test body obey an inverse square law with distance from the source
   • BBoth forces can be either attractive or repulsive
   • CBoth forces are always attractive
   • DBoth forces act only when the bodies are in contact

   (b)

   Which statement describes a difference between the two fields?

   [1 mark]

   • AOnly the electric field can be represented by field lines
   • BOnly the gravitational force obeys an inverse square law
   • COnly the gravitational force acts without contact between bodies
   • DThe gravitational force is always attractive whereas the electric force may attract or repel

   (c)

   Explain what is meant by a force field, and why a small mass near the planet and a small charge near the sphere are both described as being in a force field.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The Earth has mass 5.97 × 10²⁴ kg and the Moon has mass 7.35 × 10²² kg. Their centres are 3.84 × 10⁸ m apart. Treat both bodies as point masses at their centres.

   (a)

   Calculate the magnitude of the gravitational force of the Earth on the Moon. Use $G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$.

   [3 marks]

   (b)

   State how the force of the Moon on the Earth compares with your answer to (a), giving the physics principle that applies. Hence calculate the acceleration of the Moon towards the Earth.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Two small spheres, A of mass 2.0 kg and B of mass 8.0 kg, are fixed 0.90 m apart in deep space, far from any other mass. A third small sphere P of mass 0.50 kg lies on the straight line joining A and B.

   (a)

   Sphere P is placed on the line AB, 0.30 m from B. Calculate the magnitude of the resultant gravitational force on P and state its direction. Use $G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$.

   [6 marks]

   (b)

   Determine the distance from A of the point on line AB where the resultant force on P is zero. Explain, by considering a small displacement of P towards A from this point, whether P would be in stable or unstable equilibrium there.

   [6 marks]

   Total for question 4: 12 marks

End of questions