Question

The acceleration due to gravity on the moon is one-sixth that on earth. A high-jumper can jump 2m on earth. What height can he jump on the moon?

• A. 2 m
• B. 6 m
• C. 8 m
• D. 12 m

Answer 1

The correct option is D

12 m

Step 1 Given data:

Let:

Acceleration due to gravity on earth$=g$

Acceleration due to gravity on moon$=\frac{g}{6}$

Weight of a body on the earth =$w_e=mg$

Weight of a body on the moon =$w_m=m\times \frac{g}{6}=\frac{mg}{6}=\frac{w_e}{6}$

Height of a body achieved on the earth =$h_e=2m$

Height of a body achieved on the moon =$h_m$

Step 2 Formula used and explanation:

Due to the conservation of energy, Energy in both cases will be the same.

$$\begin{gathered} w_e{h}_e=w_m{h}_m \\ \Rightarrow h_m=\frac{w_e{h}_e}{w_m} \\ \Rightarrow h_m=\frac{w_e{h}_e}{{\displaystyle \frac{w_e}{6}}} \\ \Rightarrow h_m=6\times h_e \\ \Rightarrow h_m=6\times 2 \\ \Rightarrow h_m=12m. \end{gathered}$$

Hence, the correct option is D.