Question

The maximum vertical distance through which a full dressed astronaut can jump on the earth is 0.5 m. Estimate the maximum vertical distance through which he can jump on the moon, which has a mean density 2/3 rd that of the earth and radius one quarter that of the earth.

• A. 1.5 m
• B. 3 m
• C. 6 m
• D. 7.5 m

Answer 1

Answer: (B)

3 m

The gravitational acceleration on a planet $=g=\frac{GM}{R^2}$

$=\frac{G\rho \frac{4}{3}\pi R^3}{R^2}$ $=G\frac{4}{3}\pi \rho R\propto \rho R$

Hence the value of $g$ on moon $=g_m=\frac{g_e}{6}$

Since the astronaut has energy to jump only upto $0.5m$ on earth,

$Energy=m{g}_e{h}_e=m{g}_m{h}_m$
$⟹h_m=\frac{g_e}{g_m}{h}_e$ $=6\times h_e=3m$