Question

An object of mass 'm' when raised to height 'h' possess a potential energy of 1200J. Find the new potential energy: (a)if the same object is raised to height 'h'/4 (b)if the same object is raised to height 4'h'

Answer 1

According to the question, the potential energy at height $h$ of mass $m$ is,
$PE=mgh=1200J$
(i) When the same object is raised to height $\frac{h}{4}$ then the new potential energy of the object will be,
$$\begin{gathered} P{E}_1=mg\frac{h}{4} \\ P{E}_1=\frac{mgh}{4} \\ P{E}_1=\frac{PE}{4} \end{gathered}$$
On substituting the values we get,
$$\begin{gathered} P{E}_1=\frac{1200J}{4} \\ P{E}_1=300J \end{gathered}$$

(ii) If the same object is raised to height $4h$, then the new potential energy of the object will be,
$$\begin{gathered} P{E}_2=mg\left(4h\right) \\ P{E}_2=4mgh \\ P{E}_2=4\times PE \end{gathered}$$
On substituting the values we get,
$$\begin{gathered} P{E}_2=4\times 1200J \\ P{E}_2=4800J \end{gathered}$$