Question

Two bodies of equal weight are kept at heights of $h$ and $1.5h$ respectively. The ratio of their P.E. is

• A. $3:2$
• B. $2:3$
• C. $1:1$
• D. none of these

Answer 1

The correct option is B

$2:3$

Step 1: Given data:

The height of one body $=h$

The height of the other body $=1.5h$

The weight of both the bodies is the same.

Step 2: Calculating potential energy

As both the bodies have the same weight, consider the weight to be $mg$ , where $m$ is the mass and $g$ is the acceleration due to gravity. Now, the potential energy (P.E.) of the body kept at height $h$ is

$P.E{.}_1=mgh$

And, the potential energy of the body kept at a height $1.5h$ is

$$\begin{gathered} P.E{.}_2=mg(1.5h) \\ =1.5mgh \end{gathered}$$

Step 3: Ratio of their P.E.

$$\begin{gathered} \frac{P.E{.}_1}{P.E{.}_2}=\frac{mgh}{1.5mgh} \\ =\frac{2}{3} \end{gathered}$$

Thus, the ratio of their P.E. is $2:3$.

Hence, option B is correct.