Question

What happens to the potential energy of a body if its mass is increased by three times.

Answer 1

Definition of potential energy:

The energy possessed by a body on account of its position or configuration is called potential energy.

Mathematical expression for potential energy:

$$\begin{gathered} PotentialEnergy=mass\times accelerationduetogravity\times height \\ \therefore P.E.=m\times g\times h \end{gathered}$$

$\therefore P.E\propto m$

According to the question,

When mass is increased by three times, let the new $PotentialEnergy=P.E.\text{'}$

$P.E.\text{'}=\left(3m\right)\times g\times h=3(m\times g\times h)=3\times P.E.$

So, when mass is increased by three times, potential energy also gets increased by three times.