Question

A high jumper can jump 2.5 m on the surface of the earth he can jump on the surface of the moon to a height of

• A. 5 m
• B. 7.5 m
• C. 10 m
• D. 15 m

Answer 1

The correct option is D

15 m

Given data:

Height of the person jumping on the surface of the earth is ${\mathrm{h}}_1=2.5\mathrm{m}$

Finding the height on the surface of the moon

1. For raising the body through height h potential energy is required which is given by,

Potential energy = mass x acceleration due to gravity x height

$\mathrm{P}.\mathrm{E}=\mathrm{m}\mathrm{x}\mathrm{g}\mathrm{x}\mathrm{h}$

2. As we know that, acceleration due to gravity on the surface of the moon is given by $\frac{1}{6}$ of the acceleration due to gravity on the surface of the earth.

${\mathrm{g}}_{\mathrm{m}}=\frac{1}{6}{\mathrm{g}}_{\mathrm{e}}$

3. When the person is raised through height $\left({\mathrm{h}}_1\right)$ on the surface of the earth by gaining energy (${\mathrm{E}}_1=\mathrm{E}$).
${\mathrm{E}}_1=\mathrm{m}\mathrm{x}{\mathrm{g}}_{\mathrm{e}}\mathrm{x}{\mathrm{h}}_1$

$\mathrm{E}=\mathrm{m}\mathrm{x}{\mathrm{g}}_{\mathrm{e}}\mathrm{x}{\mathrm{h}}_1$ _{…………..(1)}
4. When the same person is raised through height $\left({\mathrm{h}}_2\right)$ on the surface of the moon by gaining the same amount of energy i.e ${\mathrm{E}}_2=\mathrm{E}$.

${\mathrm{E}}_2=\mathrm{m}\mathrm{x}{\mathrm{g}}_{\mathrm{m}}\mathrm{x}{\mathrm{h}}_2$

$\mathrm{E}=\mathrm{m}\mathrm{x}{\mathrm{g}}_{\mathrm{m}}\mathrm{x}{\mathrm{h}}_2$_{…………(2)}

5. Equating (1) and (2) we get,

${\mathrm{E}}_1={\mathrm{E}}_2$

${\mathrm{m}}_1{\mathrm{g}}_{\mathrm{e}}{\mathrm{h}}_1={\mathrm{m}}_2{\mathrm{g}}_{\mathrm{m}}{\mathrm{h}}_2$

${\mathrm{h}}_2=\frac{\mathrm{m}\mathrm{x}{\mathrm{g}}_{\mathrm{e}}\mathrm{x}{\mathrm{h}}_1}{\mathrm{m}\mathrm{x}{\mathrm{g}}_{\mathrm{m}}}=\frac{\mathrm{m}\mathrm{x}{\mathrm{g}}_{\mathrm{e}}\mathrm{x}{\mathrm{h}}_1}{\mathrm{m}\mathrm{x}{\displaystyle \frac{1}{6}}{\mathrm{g}}_{\mathrm{e}}}=6{\mathrm{h}}_1=6\mathrm{x}2.5\mathrm{m}=15\mathrm{m}$

Thus, the person on the surface of the moon will rise to the height of 15 m.

Hence, option (D) is correct.