1. What happens to the potential energy of a body if (a) mass of body is increased four times (b) the body is taken on the surface of Moon.

Dear Student,

a) If mass of a body is increased four times, we know the potential energy is given by:

$P.E.=mgh$.......(1)
After increasing the mass, we get
$P.E.\text{'}=4mgh$......(2)
Dividing (2) by (1)
we get,
$$\begin{gathered} \frac{P.E\text{'}.}{P.E.}=\frac{4mgh}{mgh} \\ P.E\text{'}.=4\times P.E. \end{gathered}$$
The new potential increases by 4 times of the original.

b) When the body is taken on the surface of Moon.

Acceleration on the moon =$\frac{1}{6}\times$acceleration on earth
$P.E.=mgh$.......(3)
After increasing the mass, we get
$P.E.\text{'}=m\frac{g}{6}h$......(2)
Dividing (2) by (1)
we get,
$$\begin{gathered} \frac{P.E\text{'}.}{P.E.}=\frac{mgh}{6\times mgh} \\ P.E\text{'}.=\frac{P.E.}{6} \end{gathered}$$
The new potential decreases by 1/6 times of the original.

Regards