Question

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

• A. 3:2
• B. 2:3
• C. 1:1
• D. 4:3

Answer 1

The correct option is B

2:3

Step 1: Given data:

$$\begin{gathered} m_1=m_2=m\left(let\right) \\ {h}_1=hand{h}_2=1.5h \end{gathered}$$

Step 2: Formula used:

Potential energy, $P.E=mgh$
Step 3: Finding ratio of P.E:

$$\begin{gathered} P.E_1=mg{h}_1=mgh \\ P.E_2=mg{h}_2=mg\times 1.5h=1.5mgh \\ Therefore,\frac{P.E_1}{P.E_2}=\frac{mgh}{1.5mgh}=\frac{1}{1.5}=\frac{2}{3}. \end{gathered}$$

Therefore, the ratio of their P. E is $\frac{2}{3}$.
Hence, the correct option is B.