Two bodies X and Y of equal masses are kept at heights of $h$ and $2 h$ respectively. What will be the ratio of their potential energies?

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Solution

Step 1.Given
$m_{X} = m_{y} = m h_{x} = h a n d h_{y} = 2 h$
Step 2.Finding PE
Potential energy of $X$ body
$P_{X} = m g h$
Potential energy of $Y$ body
$P_{Y} = m g 2 h$
$\frac{P_{x}}{P_{y}} = \frac{m g h}{m g 2 h}$
$\frac{P_{x}}{P_{y}} = \frac{1}{2}$
$P_{x} : P_{y} = 1 : 2$
Hence, the ratio of their potential energies is $1 : 2 .$

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