Gravitational fieldsAQA A-Level Physics: Topic test

20 questions, 54 marks

AQA A-Level Physics

Gravitational fields topic test

Total 54 marks

Name

Class

Date

1
Saturn's moon Titan has a mass of 1.35 × 10²³ kg and a radius of 2.57 × 10⁶ m. Treat Titan as a uniform sphere. Gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².
(a)
What is the gravitational field strength at the surface of Titan?
[1 mark]
A9.0 × 10¹² N kg⁻¹
B2.0 × 10¹⁰ N kg⁻¹
C3.5 × 10⁶ N kg⁻¹
D1.4 N kg⁻¹
(b)
What is the gravitational field strength at a height above the surface of Titan equal to the radius of Titan?
[1 mark]
A0.34 N kg⁻¹
B0.68 N kg⁻¹
C0.15 N kg⁻¹
D5.5 N kg⁻¹
(c)
A probe of mass 300 kg lands on the surface of Titan. Show that the gravitational force between Titan and the probe is about 410 N.
[2 marks]
Total for question 1: 4 marks
2
Two stars, A and B, form a binary system. Star A has a mass of 4.0 × 10³⁰ kg and star B has a mass of 1.0 × 10³⁰ kg. Their centres are 3.0 × 10¹¹ m apart. Gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².
(a)
What is the magnitude of the gravitational force between the stars?
[1 mark]
A8.9 × 10³⁸ N
B2.7 × 10⁵⁰ N
C3.0 × 10²⁷ N
D7.4 × 10²⁶ N
(b)
The mass of star B were to double and the separation of the stars were also to double. By what factor would the force between them change?
[1 mark]
A× 2
B× ½
C× ¼
D× 1
(c)
Explain why the force on star A due to star B is equal in magnitude to the force on star B due to star A, but the accelerations of the two stars are different. Calculate the acceleration of star B due to star A.
[2 marks]
Total for question 2: 4 marks
3
Mercury has a mass of 3.30 × 10²³ kg and a radius of 2.44 × 10⁶ m. Treat Mercury as a uniform sphere with no atmosphere. Gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².
(a)
Calculate the gravitational potential at the surface of Mercury, and explain the significance of the sign of your answer.
[3 marks]
(b)
A probe of mass 500 kg is raised from the surface of Mercury to a height of 2.44 × 10⁶ m above the surface. Calculate the work done on the probe.
[4 marks]
Total for question 3: 7 marks
4
Europa orbits Jupiter in a circular path of radius 6.71 × 10⁸ m with a time period of 3.55 days. Europa has a mass of 4.8 × 10²² kg. Gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².
(a)
Show that for a satellite in a circular orbit $T^2$ is proportional to $r^3$ , and use the data to calculate the mass of Jupiter.
[6 marks]
(b)
Calculate the gravitational potential at the orbit of Europa and the total energy of Europa in its orbit. Explain the significance of the sign of the total energy.
[6 marks]
Total for question 4: 12 marks
5
A uniform spherical planet has a radius of 5.0 × 10⁶ m. The gravitational field strength at its surface is 12 N kg⁻¹. Gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².
(a)
What is the mass of the planet?
[1 mark]
A4.5 × 10²⁴ kg
B9.0 × 10¹⁷ kg
C1.8 × 10²⁵ kg
D2.0 × 10⁴ kg
(b)
What is the gravitational potential at the surface of the planet?
[1 mark]
A+6.0 × 10⁷ J kg⁻¹
B−6.0 × 10⁷ J kg⁻¹
C−2.4 × 10⁻⁶ J kg⁻¹
D0 J kg⁻¹
(c)
A 40 kg load is lifted vertically through 1.0 × 10³ m near the surface of the planet. Use the gravitational field strength to calculate the change in gravitational potential and the work done on the load.
[2 marks]
Total for question 5: 4 marks
6
Engineers plan to place a communications satellite in an orbit that is synchronous with Mars, so that it stays above the same point on the Martian equator. Mars has a mass of 6.42 × 10²³ kg and takes 8.86 × 10⁴ s to rotate once. The radius of the satellite's orbit is 2.04 × 10⁷ m. Gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².
(a)
Which row gives the conditions that the orbit must satisfy?
[1 mark]
Aequatorial plane; opposite to the rotation of Mars; time period equal to the rotation period of Mars
Bpolar plane; same direction as the rotation of Mars; time period equal to the rotation period of Mars
Cequatorial plane; same direction as the rotation of Mars; time period equal to the rotation period of Mars
Dequatorial plane; same direction as the rotation of Mars; time period half the rotation period of Mars
(b)
Another satellite orbits Mars with a time period eight times as long as that of a second satellite. By what factor is the radius of its orbit greater than that of the second satellite?
[1 mark]
A× 2
B× 8
C× 64
D× 4
(c)
Calculate the orbital speed of the satellite.
[2 marks]
Total for question 6: 4 marks
7
Venus has a mass of 4.87 × 10²⁴ kg and a radius of 6.05 × 10⁶ m. Treat Venus as a uniform sphere with no atmosphere. Gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².
(a)
Calculate the escape velocity from the surface of Venus.
[3 marks]
(b)
A probe of mass 600 kg is in a circular orbit at a height of 3.0 × 10⁶ m above the surface of Venus. Calculate the minimum extra energy that must be given to the probe so that it can escape from Venus.
[4 marks]
Total for question 7: 7 marks
8
Ganymede has a mass of 1.48 × 10²³ kg and a radius of 2.63 × 10⁶ m. A probe is launched vertically from its surface at 1.5 × 10³ m s⁻¹. Ignore any atmosphere and the rotation of Ganymede. Gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².
(a)
Calculate the gravitational field strength at the surface of Ganymede and the escape speed. Explain why the probe, launched at 1.5 × 10³ m s⁻¹, cannot escape.
[6 marks]
(b)
Calculate the maximum height above the surface reached by the probe. Compare your answer with the height predicted by assuming a uniform field equal to the surface value, and explain the difference.
[6 marks]
Total for question 8: 12 marks

End of questions

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).