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
Answer
Why
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.
Why the others are wrong
- (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.
Concept
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.
Key facts
- 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.
Study next
Common traps
- 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.
Related PYQs
No directly related past PYQ was found.
Practice
- 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.