Question

A particle falls from rest under gravity. which of the following graphs correctly shows the variation of
(i) its potential energy with respect to the ground against time and
(ii) its kinetic energy against time

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Potential energy of a particle at a height h from the earth's surface is

$PE=mgh$

Now, as the particle falls from rest under gravity, its height will change with time (t) as

$h^{\prime }=h-\frac{1}{2}g{t}^2\therefore PE=mg(h-\frac{1}{2}a{t}^2)$

Now, kinetic energy of the particle is

$KE=\frac{1}{2}m{v}^2$

As the particle falls from rest under gravity, speed of the particle changes as $v=gt$

$\therefore KE=\frac{1}{2}m{g}^2{t}^2(\because u=0)$

So graph between Kinetic energy and time will be parabolic in nature