Suppose, a ball of mass M is thrown upwards from a point A and it reaches up to the highest point B and returns back to point A, which one among the following is correct?
- (a)Kinetic Energy at A = Potential Energy at B
- (b)Kinetic Energy at A = Potential Energy at A
- (c)Kinetic Energy at B = Potential Energy at B
- (d)Kinetic Energy at B = Kinetic Energy at A
Answer
Why
Correct — A, Kinetic Energy at A = Potential Energy at B. Take A (the launch point) as the reference where the potential energy is zero. At A the ball has only kinetic energy (half M v squared) and no potential energy; at the top B it is momentarily at rest, so it has only potential energy (M g h) and no kinetic energy. Since mechanical energy is conserved (ignoring air resistance), all the kinetic energy at A has turned into potential energy at B — so KE at A = PE at B.
Why the others are wrong
- (b)Kinetic Energy at A = Potential Energy at A — At the launch point A the height is zero, so the potential energy at A is zero while the kinetic energy at A is large — they cannot be equal unless the ball is not moving at all.
- (c)Kinetic Energy at B = Potential Energy at B — At the highest point B the ball is momentarily at rest, so its kinetic energy is zero; it cannot equal the non-zero potential energy at B.
- (d)Kinetic Energy at B = Kinetic Energy at A — Kinetic energy at B is zero (the ball stops at the top) whereas kinetic energy at A is the full launch value, so they are not equal; only when the ball returns to A does its kinetic energy match the launch value.
Concept
For a body moving under gravity with negligible air resistance, mechanical energy (kinetic plus potential) is conserved. As the ball rises, kinetic energy converts to potential energy; at the highest point the speed is zero so the energy is all potential; on the way down potential energy converts back to kinetic. Measuring potential energy from the launch level A makes the potential energy at A zero.
Track the two energies at the two points. Bottom (A): all kinetic, no potential. Top (B): no kinetic, all potential. Conservation makes KE at A equal PE at B. This is the same potential-to-kinetic trade-off that governs a pendulum swing or a planet in orbit (fastest where it is lowest or closest).
Key facts
- Conservation of mechanical energy: kinetic plus potential energy stays constant when only gravity acts (no friction or air drag).
- At the launch point A (the reference level) the potential energy is zero, so the ball's energy is purely kinetic.
- At the highest point B the velocity is zero, so the kinetic energy is zero and the energy is purely potential.
- Returning to A the ball regains its original kinetic energy and speed, by conservation.
Study next
Common traps
- Forgetting that the potential energy at the launch level A is zero — you must fix a reference level.
- Thinking the kinetic energy at the top is non-zero — the ball is momentarily at rest at B.
Asked by comparing kinetic and potential energy at the bottom and top of vertical motion, or as a numerical using half m v squared equals m g h.
Related PYQs
The planet Mercury is revolving in an elliptical orbit around the Sun as shown in the given figure. The kinetic energy of Mercury is greatest at the point labelled
- (a) A
- (b) B
- (c) C
- (d) D
Answer(a) A — the point nearest the Sun (perihelion)
The same kinetic-to-potential energy trade-off under conservation: the planet moves fastest (maximum kinetic energy) where it is nearest the Sun and its gravitational potential energy is least — the orbital analogue of a ball having all kinetic energy at the bottom and all potential energy at the top.
Practice
- practice — not a real PYQ
A ball thrown vertically upward has, at its highest point,
- (a)Maximum kinetic energy
- (b)Zero kinetic energy
- (c)Zero potential energy
- (d)Maximum speed
Answer(b) Zero kinetic energy — it is momentarily at rest, so the energy is all potential. - practice — not a real PYQ
A stone of mass m is thrown up with speed v. Ignoring air resistance, the maximum height reached is
- (a)v squared / 2g
- (b)v / 2g
- (c)2 v squared / g
- (d)v squared / g
Answer(a) v squared / 2g — from half m v squared = m g h.