When a ball bounces off the ground, which of the following changes suddenly? (Assume no loss of energy to the floor)
- (a)Its speed
- (b)Its momentum
- (c)Its kinetic energy
- (d)Its potential energy
Answer
Why
Correct — B, its momentum. Momentum is a vector, p = mv. When the ball rebounds with no energy loss its speed is unchanged but its direction of travel reverses (downward becomes upward), so the momentum vector flips from −mv to +mv — a sudden change of 2mv delivered by the floor's impulse. Speed and kinetic energy depend only on the magnitude of the velocity, so they stay the same, and at the moment of contact the height (hence the gravitational potential energy) is essentially unchanged.
Why the others are wrong
- (a)Its speed — Speed is the magnitude of velocity; with no energy lost the ball leaves at the same speed it arrived, so speed does not change.
- (c)Its kinetic energy — Kinetic energy ½mv² depends only on speed; since the speed is unchanged (no loss to the floor) the kinetic energy is the same before and after.
- (d)Its potential energy — At the floor the ball is at the same height just before and just after the bounce, so its gravitational potential energy does not change suddenly.
Concept
Velocity and momentum are vectors; speed, kinetic energy and potential energy are scalars. A bounce reverses the direction of motion, so the vector quantities change even when their magnitudes stay the same, while scalar quantities that depend only on magnitude do not.
The trap is that 'no energy lost' suggests nothing changes — but reversing direction alone changes a vector. The change of momentum, 2mv, is exactly the impulse the floor delivers during contact.
Key facts
- Momentum p = mv is a vector quantity.
- An elastic bounce reverses the velocity direction, changing momentum by 2mv.
- Speed and kinetic energy (scalars) are unchanged when no energy is lost.
- The floor exerts an impulse equal to the change in momentum during contact.
Direction reverses, so the vector momentum flips by 2mv while the scalar speed and kinetic energy stay the same.
Study next
Common traps
- Assuming 'no energy loss' means nothing at all changes — the direction of momentum still reverses.
- Treating momentum as a scalar and missing the direction reversal.
Asked as 'what changes when a ball bounces' — sort each option into vector (changes with direction) or scalar (unchanged if magnitude is fixed).
Related PYQs
A ball of 0·1 kg mass is dropped on a hard floor from a height of 0·45 m and rises to a height of 0·20 m. If it was in touch with the floor for 0·1 s, the net force it applied on the floor while bouncing is : (take the gravitational acceleration g = 10 m s⁻²)
- (a) 1·0 N
- (b) 6·0 N
- (c) 3·0 N
- (d) 5·0 N
Answer(d) 5·0 N
Same concept — the bounce changes the ball's momentum. That NDA item makes you compute the impulse (change of momentum ÷ contact time = force) of a rebounding ball; this one asks which quantity changes suddenly, namely the momentum.
Practice
- practice — not a real PYQ
A ball of mass m hits a wall normally with speed v and rebounds with the same speed. The change in its momentum is
- (a)0
- (b)mv
- (c)2mv
- (d)½mv²
Answer(c) 2mv — the velocity reverses, so momentum changes from −mv to +mv. - practice — not a real PYQ
Which of the following is a scalar quantity?
- (a)Velocity
- (b)Momentum
- (c)Speed
- (d)Force
Answer(c) Speed — it has magnitude only, unlike the vector quantities listed.