Question

Two bodies A and B of equal masses are kept at heights of h and 2h respectively. What will be the ratio of their potential energy?

Answer 1

Mass of body A, $m_1=m$
Mass of body B, $m_2=m$
Height $h_1=h$
Height $h_2=2h$

Acceleration due to gravity, $g_1=g$
Acceleration due to gravity, $g_2=g$

$\frac{PotentialEnergy(P.E_1)}{PotentialEnergy(P.E_2)}=?$
$P.E=mgh$

$\Rightarrow P.E\alpha h$
($\therefore$ 'm' and 'g' are constants)

$\Rightarrow \frac{P.E_1}{P.E_2}=\frac{h_1}{h_2}$

$\Rightarrow \frac{P.E_1}{P.E_2}=\frac{h}{2h}\Rightarrow \frac{P.E_1}{P.E_2}=\frac{1}{2}$
Therefore, the ratio of potential energy is of the two bodies is 1 : 2.