Question

The decrease in the potential energy of a ball of mass $20kg$ which falls from a height of $50cm$ is
(A) $968J$
(B) $98J$
(C) $1980J$
(D) None of these

Answer 1

Hint: We know that the potential energy of a falling body is due to gravity and called gravitational potential energy here, we will use the general formula of the gravitational potential energy of a falling body and using the value of given parameters value, we will solve for the potential energy of the given ball.

Formula Used:
If m is the mass of a body, g is the acceleration due to gravity and h is the height of a body from the surface of the earth then, the potential energy of the body is calculated as
$P.E = mgh$

Complete answer:
We have given that the a ball of mass $m = 20kg$ falls from a height of $h = 50cm = 0.5m$ towards the ground with acceleration due to gravity $g = 9.8m{s^{ - 2}}$.

Now change in potential energy due to change in height so initial height is $h = 0.5m$ and final height is zero as ball hits the ground so, Decrease in potential energy is calculated by using the formula $P.E = mgh$ we get
$
  P.E = 20(9.8)0.5 \\
  P.E = 98J \\
 $
So, the change in potential energy of the falling ball is $98J$

Hence, the correct answer is option (B) $98J$

Note: Here, the units of height are converted using a conversion relation of $1cm = 0.01m$ and gravitational potential energy is the energy possessed by the body when its position is changed in the gravitational field also sometimes for easier calculation the approximate value of acceleration due to gravity is taken as $g = 10m{s^{ - 2}}$.