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 — C, 1 : 1. The two planets pull on each other with a single mutual gravitational force. By Newton's law of gravitation, F = G x M1 x M2 / r^2 — an expression symmetric in the two masses and using the one centre-to-centre distance r — so the force on planet 1 due to planet 2 equals in magnitude the force on planet 2 due to planet 1. Newton's third law says the same: action and reaction are equal and opposite. The mass ratio (1 : 7) and diameter ratio (2 : 1) are red herrings, so the ratio of forces is 1 : 1.
- (a)1 : 7 — This is merely the mass ratio. The forces on the two bodies are equal; it is their accelerations (a = F/m) that would differ in the ratio of masses, not the forces.
- (b)7 : 1 — The reverse mass ratio — the same mistake of treating the mutual force as if it were proportional to mass.
- (d)2 : 1 — This is the diameter ratio. Diameters do not set the mutual force, and even the separation r is common to both bodies, so it cancels.
The gravitational attraction between two bodies is a single interaction: each body feels a pull equal in magnitude and opposite in direction (Newton's third law), whatever their masses or sizes. Their resulting accelerations differ — the lighter body accelerates more — but the forces are always equal.
The trap is the intuition that a much heavier planet 'should' exert a larger force. It does not: mass asymmetry changes the accelerations, not the equal-and-opposite forces. This is why the Earth pulls an apple down with exactly the force the apple pulls the Earth up.
- Newton's law of gravitation: F = G x M1 x M2 / r^2 — symmetric in both masses, so each body feels the same magnitude of force.
- Newton's third law: to every action there is an equal and opposite reaction.
- Equal forces but unequal accelerations: a = F/m, so the lighter body accelerates more.
- The Earth attracts an apple with exactly the force the apple attracts the Earth.
- Equating the ratio of forces with the ratio of masses.
- Assuming the bigger or heavier body exerts the larger force.
Asked as a 'ratio of forces two bodies exert on each other' trap in which the mass and size data are deliberate red herrings.
No directly related past PYQ was found.
- practice — not a real PYQ
The Earth attracts a falling stone. Compared with this, the force the stone exerts on the Earth is
- (a)much smaller
- (b)much larger
- (c)equal in magnitude
- (d)zero
Answer(c) equal in magnitude — action and reaction are equal and opposite.
- practice — not a real PYQ
Two bodies of unequal mass exert equal gravitational forces on each other. Which body experiences the greater acceleration?
- (a)the heavier body
- (b)the lighter body
- (c)both equally
- (d)neither
Answer(b) the lighter body — for equal force, a = F/m is larger when m is smaller.