Two bodies of mass M each are placed R distance apart. In another system, two bodies of mass 2M are placed R/2 distance apart. If F be the gravitational force between the bodies in the first system, then the gravitational force between the bodies in the second system will be
- (a)16 F
- (b)1 F
- (c)4 F
- (d)None of the above
Correct — A, 16 F. Newton's law of gravitation gives F = G·m1·m2/r². In the first system F = G·M·M/R² = GM²/R². In the second system each mass is 2M and the separation is R/2, so F' = G·(2M)(2M)/(R/2)² = G·4M²/(R²/4) = 16·GM²/R² = 16 F. The mass product grows fourfold and 1/r² grows fourfold, so together they multiply the force by 16.
- (b)1 F — The force stays the same only if both the mass product and the distance are effectively unchanged; here both change and multiply the force sixteenfold.
- (c)4 F — Multiplying only the mass product (2M x 2M = 4x) gives 4F, but the distance is also halved, which multiplies the force by a further 4 — the total is 16F, not 4F.
- (d)None of the above — 16 F is a listed and correct value, so 'none of the above' is wrong.
Newton's law of universal gravitation states that the force between two point masses is F = G·m1·m2/r² — proportional to the product of the masses and inversely proportional to the square of the distance between them. Scaling the masses and the distance therefore scales the force in a predictable way.
Change the two factors separately: doubling each mass multiplies the product by 4, and halving the distance multiplies 1/r² by 4. Multiplying the two effects gives an overall factor of 16, so F becomes 16 F.
- Newton's law of gravitation: F = G·m1·m2/r².
- Force is proportional to the product of the masses and inversely proportional to the square of the separation.
- Doubling each mass multiplies the force by 4; halving the distance multiplies it by 4 again — a total of 16.
- G is the universal gravitational constant, about 6.67 x 10 to the power -11 N·m²/kg².
Mass product x4 and 1/r² x4 give a x16 change — option (a).
- Changing only the masses and forgetting that the distance also changed.
- Forgetting the inverse-square: halving r multiplies the force by 4, not 2.
Asked by scaling the masses and/or separation and finding the new gravitational force as a multiple of F.
No directly related past PYQ was found.
- practice — not a real PYQ
If the distance between two masses is halved (masses unchanged), the gravitational force becomes
- (a)half
- (b)double
- (c)four times
- (d)one-fourth
Answer(c) four times — force varies as 1/r², so halving r multiplies it by 4.
- practice — not a real PYQ
The SI unit of the universal gravitational constant G is
- (a)N
- (b)N·m²/kg²
- (c)N·kg²/m²
- (d)N/m²
Answer(b) N·m²/kg² — obtained by rearranging F = G m1 m2 / r².