Two bodies of unequal masses are dropped from a tower. At any instant, they have equal
- (a)Momentum
- (b)Acceleration
- (c)Potential energy
- (d)Kinetic energy
Correct — B, Acceleration. Bodies in free fall accelerate at g regardless of their mass (ignoring air resistance), so at any instant both bodies share the same acceleration. Momentum (mv), potential energy (mgh) and kinetic energy ((1/2)mv^2) all depend on mass and therefore differ for the two unequal masses.
- (a)Momentum — Momentum p = mv, so at the same instant the heavier body has greater momentum — it is not equal for the two masses.
- (c)Potential energy — Potential energy = mgh depends on mass, so the two unequal masses have different potential energies at the same height.
- (d)Kinetic energy — Kinetic energy = (1/2)mv^2; even though both have the same speed at a given instant, the larger mass has greater kinetic energy.
In free fall near the Earth's surface, all objects experience the same downward acceleration g (about 9.8 m/s^2), independent of mass — Galileo's result. So two objects dropped together fall with identical velocity and acceleration at each instant, but any quantity that includes mass — momentum, kinetic energy, potential energy — differs between unequal masses.
The trap is to assume the heavier body 'falls faster'. It does not — acceleration and speed are mass-independent in free fall. Only mass-independent quantities (velocity, acceleration, time of fall) are equal; mass-weighted ones are not.
- In free fall (no air resistance) all bodies accelerate at g, independent of mass.
- Two unequal masses dropped together have equal acceleration and equal velocity at each instant.
- Momentum (mv), kinetic energy ((1/2)mv^2) and potential energy (mgh) all depend on mass and differ.
- This is why a feather and a coin fall together in a vacuum.
Only acceleration (g) is mass-independent, so only it is equal for the two bodies — option (b).
- Heavier does not mean faster in free fall — the acceleration is the same g.
- Only mass-independent quantities are equal; mv, (1/2)mv^2 and mgh are not.
Asks which quantity is equal or different for unequal masses in free fall, testing the mass-independence of g.
No directly related past PYQ was found.
- practice — not a real PYQ
In the absence of air resistance, a heavy stone and a light feather dropped from the same height will
- (a)reach the ground together
- (b)the stone reaches first
- (c)the feather reaches first
- (d)neither reaches the ground
Answer(a) reach the ground together — both accelerate at the same g.
- practice — not a real PYQ
Two bodies of different masses fall freely from the same height. At any instant they have the same
- (a)kinetic energy
- (b)momentum
- (c)velocity
- (d)potential energy
Answer(c) velocity — velocity (like acceleration) is independent of mass in free fall.