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
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.
- (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.
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).
- 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.
- 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.
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 — 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.