The masses of two planets are in the ratio of 1 : 7. The ratio between their diameters is 2: 1. The ratio of forces which they exert on each other is
- A.1:7
- B.7:1
- C.1:1
- D.2:1
Correct answer
Explanation
The correct answer is C, 1:1. By Newton's third law, the gravitational force that the first planet exerts on the second is equal and opposite to the force the second exerts on the first.
Newton's law of gravitation gives a single force, F = Gm₁m₂/r², acting between two bodies, where r is the distance between their centres. That one force acts on both bodies, pulling each towards the other, so whatever their masses or sizes, the two forces form an action-reaction pair of the same size. The masses (1 : 7) and diameters (2 : 1) change how strongly each planet accelerates, not the size of the mutual force.
A is wrong because 1 : 7 is the ratio of the masses, not of the forces.
B is wrong because 7 : 1 simply inverts the mass ratio; the forces are still equal.
D is wrong because 2 : 1 is the ratio of the diameters, which does not decide the mutual force.
Exam tip: the Earth pulls an apple exactly as hard as the apple pulls the Earth; only their accelerations differ.
Practice Questions
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- B.Martin Luther
- C.Johannes Kepler
- D.Copernicus
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In 1609 Kepler showed that the planets move around the Sun in elliptical orbits, with the Sun at one focus of the ellipse.
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