Maximum Marks: 40Suggested time: 60 minutes
Instructions: Answer all 20 questions. Marks are shown in brackets. Show calculation steps and units. These are original practice questions, not an official examination paper.
Section A · 1-mark questions — 8 × 1 = 8 marks
- Kepler's law of equal areas?[1]
- Universal gravitation law?[1]
- SI unit of G?[1]
- g at surface of a spherical planet?[1]
- Gravitational potential energy zero at infinity?[1]
- Does escape speed depend on launched mass?[1]
- What supplies centripetal force to a satellite?[1]
- Kepler's third law for fixed central mass?[1]
Section B · 2-mark questions — 6 × 2 = 12 marks
- Force between 2 kg and 3 kg 1 m apart; G=6.67×10⁻¹¹.[2]
- Weight of 50 kg for g=9.8?[2]
- If orbit radius doubles, circular-speed factor?[2]
- At altitude h=R, ratio g_h/g?[2]
- Approximate potential-energy change for small height h?[2]
- If orbital radius becomes 4r, period factor?[2]
Section C · 3-mark questions — 4 × 3 = 12 marks
- Find g at height h=R/2 relative to surface g.[3]
- Escape speed for g=5 m/s² and R=2×10⁶ m?[3]
- GM=4×10¹⁴, r=7×10⁶ m: orbital speed?[3]
- Weight is 600 N at surface. Weight at h=R?[3]
Section D · 4-mark questions — 2 × 4 = 8 marks
- Derive circular orbital speed and period.[4]
- 1000 kg satellite at r=7×10⁶ m, GM=4×10¹⁴. Find speed and energy.[4]
End of paper — review signs, units and working.
Open marking scheme and model answers
Attempt the paper before opening the key. Model answers show the expected facts and results; mark allocation is a suggested guide and equivalent correct methods should receive credit.
Q1 · 1 mark
The radius vector sweeps equal areas in equal times.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q2 · 1 mark
F=Gm₁m₂/r².
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q3 · 1 mark
N m² kg⁻².
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q4 · 1 mark
g=GM/R².
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q5 · 1 mark
U=−GMm/r.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q6 · 1 mark
No.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q7 · 1 mark
Gravity.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q8 · 1 mark
T²∝r³.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.
Q9 · 2 marks
4.00×10⁻¹⁰ N.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.
Q10 · 2 marks
490 N.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.
Q11 · 2 marks
1/√2.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.
Q12 · 2 marks
1/4.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.
Q13 · 2 marks
ΔU=mgh.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.
Q14 · 2 marks
8.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.
Q15 · 3 marks
g_h/g=(2/3)²=4/9.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.
Q16 · 3 marks
√(2gR)=4.47×10³ m/s.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.
Q17 · 3 marks
√(GM/r)≈7.56×10³ m/s.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.
Q18 · 3 marks
150 N.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.
Q19 · 4 marks
GMm/r²=mv²/r ⇒ v=√(GM/r); T=2πr/v=2π√(r³/GM).
Suggested split: 1 for principle, 1 for equation, 1 for working and 1 for result/explanation. Accept an equivalent correct method.
Q20 · 4 marks
v≈7.56×10³ m/s; E=−GMm/(2r)≈−2.86×10¹⁰ J.
Suggested split: 1 for principle, 1 for equation, 1 for working and 1 for result/explanation. Accept an equivalent correct method.