The questions are on the gravitational field test. Take it under real conditions before reading the mark scheme.
Quick answer: Newton's law of gravitation says two masses attract with force F = G m₁m₂/r². This mark scheme gives the model answers and the marks for the 8 questions of the Physics 11-12 test on gravitational field, from field strength definition to negative potential, with the equivalent answers to accept.
The model answers give the method and the final answer in bold. Marks are awarded for the correct equation and substitution as well as the result, so show each step. Check units and that r is measured from the centre.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB D.1
Question 1 Field strength definition (2 marks)
Gravitational field strength is the gravitational force per unit mass acting on a small test mass at that point. It is directed towards the centre of the source mass.Marking: 1 mark for force per unit mass; 1 mark for direction towards the source.
Question 2 Mars (3 marks)
- g = G M ÷ R² = 6.67 × 10⁻¹¹ × 6.42 × 10²³ ÷ (3.39 × 10⁶)² = 3.73 N/kg.
- W = m g = 70 × 3.73 = 261 N.
Marking: (a) 1 mark for the formula, 1 for the result; (b) 1 mark.
Question 3 Satellite orbit (3 marks)
- G M m ÷ r² = m v² ÷ r, so v = √(G M ÷ r) = √(3.98 × 10¹⁴ ÷ 7.2 × 10⁶) = 7.4 km/s.
- T = 2π r ÷ v = 2π × 7.2 × 10⁶ ÷ 7437 = 6083 s = 1.7 h.
Marking: (a) 1 mark for equating forces, 1 for the result; (b) 1 mark.
Question 4 Kepler’s third law (3 marks)
- The square of the orbital period is proportional to the cube of the orbital radius.
- T² ∝ r³, so TB = 200 × 4^(3/2) = 200 × 8 = 1600 days.
Marking: (a) 1 mark; (b) 1 mark for the ratio, 1 for the result.
Question 5 Potential graph (3 marks)
- V = −G M ÷ R = −3.98 × 10¹⁴ ÷ 6.37 × 10⁶ = −62.5 MJ/kg.
- At 2R, V = −31.3 MJ/kg. Energy = m ΔV = 1.0 × (−31.3 − (−62.5)) = 31 MJ.
Marking: (a) 1 mark; (b) 1 mark for reading V at 2R, 1 mark for the difference.
Question 6 Escape speed of Venus (3 marks)
- v = √(2 G M ÷ R) = √(2 × 6.67 × 10⁻¹¹ × 4.87 × 10²⁴ ÷ 6.05 × 10⁶) = 10.4 km/s.
- The kinetic energy ½ m v² and the potential energy G M m ÷ R both contain m, so m cancels.
Marking: (a) 1 mark for the formula, 1 for the result; (b) 1 mark.
Question 7 Weightlessness (2 marks)
The astronauts and the spacecraft are in free fall with the same acceleration, so there is no contact force between them. They feel weightless because weight is sensed through contact forces.Marking: 1 mark for gravity acts and both fall together; 1 mark for no contact force.
Question 8 Negative potential (1 mark)
It is defined as zero at infinity and gravity is attractive, so work must be done to move a mass out to infinity, which means the potential is below zero.Marking: 1 mark for zero at infinity with attraction.
