Gravitational fieldsEdexcel A-Level Physics: Topic test

1. 1
   A uniform spherical planet P has mass 3.2 × 10²⁴ kg and radius 5.0 × 10⁶ m. Take G = 6.67 × 10⁻¹¹ N m² kg⁻².

   (a)

   What is the gravitational field strength at the surface of P?

   [1 mark]

   • A4.3 × 10⁷ N kg⁻¹
   • B0.85 N kg⁻¹
   • C17 N kg⁻¹
   • D8.5 N kg⁻¹

   (b)

   What is the gravitational field strength at a height of 5.0 × 10⁶ m above the surface of P?

   [1 mark]

   • A4.3 N kg⁻¹
   • B2.1 N kg⁻¹
   • C1.1 N kg⁻¹
   • D8.5 N kg⁻¹

   (c)

   Calculate the gravitational force on an astronaut of mass 60 kg standing on the surface of P.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Europa, a moon of Jupiter, may be treated as a uniform sphere of mass 4.80 × 10²² kg and radius 1.56 × 10⁶ m. Take G = 6.67 × 10⁻¹¹ N m² kg⁻².

   (a)

   What is the gravitational potential at the surface of Europa?

   [1 mark]

   • A−2.05 × 10⁶ J kg⁻¹
   • B+2.05 × 10⁶ J kg⁻¹
   • C−1.32 J kg⁻¹
   • D−4.10 × 10⁶ J kg⁻¹

   (b)

   What is the gain in gravitational potential energy of a probe of mass 1500 kg that is moved from the surface of Europa to infinity?

   [1 mark]

   • A−3.1 × 10⁹ J
   • B2.1 × 10⁶ J
   • C3.1 × 10⁹ J
   • D6.2 × 10⁹ J

   (c)

   Explain why the gravitational potential at any point near a planet is negative.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Two protons are 2.0 × 10⁻¹⁵ m apart in a nucleus. Mass of a proton = 1.67 × 10⁻²⁷ kg. Charge of a proton = 1.60 × 10⁻¹⁹ C. G = 6.67 × 10⁻¹¹ N m² kg⁻². $\dfrac{1}{4\pi\varepsilon_0}$ = 8.99 × 10⁹ N m² C⁻².

   (a)

   Calculate the gravitational force between the two protons.

   [3 marks]

   (b)

   Calculate the electrostatic force between the two protons and how many times greater it is than the gravitational force. State one similarity and one difference between the two forces.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A weather satellite of mass 1500 kg is in a circular orbit of radius 6.80 × 10⁶ m about the Earth. The orbit is later raised to a circular orbit of radius 1.36 × 10⁷ m. For the Earth, GM = 3.98 × 10¹⁴ m³ s⁻².

   (a)

   Explain how the kinetic energy, the gravitational potential energy and the orbital period of the satellite change when it moves to the higher orbit, and why the engines must supply energy.

   [6 marks]

   (b)

   Calculate the orbital speed of the satellite in the lower orbit. Calculate the energy that the engines must supply to raise the satellite to the higher orbit.

   [6 marks]

   Total for question 4: 12 marks

5. 5
   Jupiter's moon Io moves in a circular orbit of radius 4.22 × 10⁸ m about the centre of Jupiter, with a period of 1.77 days (1.53 × 10⁵ s). Take G = 6.67 × 10⁻¹¹ N m² kg⁻².

   (a)

   What is the orbital speed of Io?

   [1 mark]

   • A2.8 × 10³ m s⁻¹
   • B1.7 × 10⁴ m s⁻¹
   • C1.1 × 10⁵ m s⁻¹
   • D8.7 × 10³ m s⁻¹

   (b)

   What is the centripetal acceleration of Io?

   [1 mark]

   • A4.1 × 10⁻⁵ m s⁻²
   • B1.4 m s⁻²
   • C7.1 × 10⁻² m s⁻²
   • D0.71 m s⁻²

   (c)

   Calculate the mass of Jupiter.

   [2 marks]

   Total for question 5: 4 marks

6. 6
   Planet Q orbits the Sun in a circular orbit of radius 4.0 times the radius of the Earth's orbit. The Earth's orbital period is 1.0 year.

   (a)

   What is the orbital period of Q?

   [1 mark]

   • A4.0 years
   • B2.0 years
   • C8.0 years
   • D16 years

   (b)

   What is the orbital speed of Q divided by the orbital speed of the Earth?

   [1 mark]

   • A0.50
   • B0.25
   • C2.0
   • D0.125

   (c)

   Explain why the orbital period of a planet does not depend on the mass of the planet.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   Titan, a moon of Saturn, may be treated as a uniform sphere of mass 1.35 × 10²³ kg and radius 2.58 × 10⁶ m. A lander of mass 320 kg is lifted from the surface of Titan to a height of 1.0 × 10⁶ m. Take G = 6.67 × 10⁻¹¹ N m² kg⁻².

   (a)

   Calculate the gravitational potential at the surface of Titan and at a height of 1.0 × 10⁶ m above the surface.

   [3 marks]

   (b)

   Calculate the increase in gravitational potential energy of the lander. Explain why using mgh with the surface value of g gives a different answer, and state whether it is larger or smaller.

   [4 marks]

   Total for question 7: 7 marks

8. 8
   A student compares the gravitational field of a small planet with the electric field of a charged conducting sphere. The planet has mass 6.0 × 10²² kg and radius 1.5 × 10⁶ m. The sphere carries a charge of +4.0 × 10⁻⁶ C and has a radius of 0.20 m. Both may be treated as point sources at their centres. G = 6.67 × 10⁻¹¹ N m² kg⁻². $\dfrac{1}{4\pi\varepsilon_0}$ = 8.99 × 10⁹ N m² C⁻².

   (a)

   Discuss the similarities and differences between gravitational fields and electric fields.

   [6 marks]

   (b)

   Calculate the gravitational field strength at the surface of the planet and the electric field strength at the surface of the sphere. Calculate the potential at each surface. State what happens to each field strength when the distance from the centre is doubled, and explain why the potentials have opposite signs.

   [6 marks]

   Total for question 8: 12 marks

End of questions