Newton's law of gravitation between two point masses is F = Gm₁m₂/r² and gravitational field strength is force per unit mass, so this Year 13 sheet opens with the field law and its definition. The key records 9.8 N kg⁻¹ at the surface and g ∝ 1/r².
Key Takeaways
Gravitational force is F = Gm₁m₂/r² (Q1).
Gravitational field strength is force per unit mass (Q2).
Q3 records 9.8 N kg⁻¹ as the field strength.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.Newton's law of gravitation gives the force between two point masses m₁ and m₂ separated by r as...
(a) F = Gm₁m₂/r(b) F = Gm₁m₂/r²(c) F = Gm₁m₂r²(d) F = Gm₁m₂
2.Gravitational field strength is defined as...
(a) force per unit mass(b) force per unit charge(c) energy per unit mass(d) mass per unit volume
3.The gravitational field strength at the surface of the Earth is approximately...
(a) 9.8 N kg⁻¹(b) 6.7 N kg⁻¹(c) 1.6 N kg⁻¹(d) 980 N kg⁻¹
4.For a point mass, the gravitational field strength varies with distance r as...
(a) g ∝ r(b) g ∝ r²(c) g ∝ 1/r(d) g ∝ 1/r²
5.The gravitational potential at a point is...
(a) always positive(b) negative and zero at infinity(c) always zero(d) measured in newtons
6.If both masses in a gravitational pair are doubled and the distance between them is doubled, the force between them...
(a) doubles(b) quadruples(c) stays the same(d) halves
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.State Newton's law of gravitation.
8.Define gravitational field strength and give its SI unit.
9.Define gravitational potential at a point.
10.Explain why gravitational potential is negative.
11.How does the gravitational field strength of a point mass vary with distance from the mass?
12.What is meant by a radial gravitational field?
13.Describe what is meant by a geostationary orbit.
14.Explain why an astronaut in orbit around the Earth experiences apparent weightlessness.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.Two masses of 1000 kg each are separated by 2 m. Using F = Gm₁m₂/r² with G = 6.67×10⁻¹¹ N m² kg⁻², calculate the gravitational force between them.
16.Using g = GM/R², calculate the gravitational field strength at the Earth's surface given M = 6.0×10²⁴ kg and R = 6.4×10⁶ m.
17.At a point a height h = R above the Earth's surface the distance from the centre is 2R. Given g = 9.8 N kg⁻¹ at the surface and g ∝ 1/r², calculate g at that height.
18.A satellite orbits at a radius of 8×10⁶ m from the Earth's centre. Using v = √(GM/r) with GM = 4.0×10¹⁴ N m² kg⁻¹, calculate the orbital speed and the period using T = 2πr/v.
19.A 100 kg satellite sits on the Earth's surface. Using Ep = -GMm/R with GM = 4.0×10¹⁴ N m² kg⁻¹ and R = 6.4×10⁶ m, calculate its gravitational potential energy.
20.Two masses of 2×10⁶ kg and 3×10⁶ kg are separated by 1 km. Using F = Gm₁m₂/r² with G = 6.67×10⁻¹¹ N m² kg⁻², calculate the gravitational force between them.
Answer Key
1. b) F = Gm₁m₂/r²
2. a) force per unit mass
3. a) 9.8 N kg⁻¹
4. d) g ∝ 1/r²
5. b) negative and zero at infinity
6. c) stays the same
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
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20. Refer to solution guide.
End of Worksheet
People Also Ask
What is Newton's law of gravitation?
F = Gm₁m₂/r², option (b) in this worksheet (Q1).
What is gravitational field strength?
Force per unit mass, option (a) in this worksheet (Q2).
How does g depend on distance?
g ∝ 1/r², option (d) in this worksheet (Q4).
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