Question

A body is falling from a height $h$. After it has fallen a height $h/2$, it will possess:

• A. only potential energy
• B. only kinetic energy
• C. half potential and half kinetic energy
• D. more kinetic and less potential energy

Answer 1

The correct option is C half potential and half kinetic energy

Let a body of mass ${}^{\prime }{m}^{\prime }$ placed at a height ${}^{\prime }{h}^{\prime }$ above the ground, start falling down from rest.`
When the body falls from a height $h$ to $h/2$, the potential energy is given as $\frac{mgh}{2}$.
The body covers the distance $h/2$ with a velocity $v$. We make use of the third equation of motion to obtain velocity of the body.

$v^2-u^2=2aS$

Here, $u=0,a=g$ and $S=x$

$v^2-0=\frac{2gh}{2},thatis{v}^2=gh$

Kinetic energy = $\frac{1}{2}m{v}^2$

That is, $K.E=\frac{mgh}{2}$

Hence, at height h/2 the energy possessed is half potential energy and half the kinetic energy.