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 $\frac{2}{3}$ 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

Answer 2

On moon $g_{m} =\frac{4}{3} \pi g\left(\frac{R}{4}\right)\left(\frac{2 \rho}{3}\right)$ $=\frac{1}{6}\left(\frac{4}{3} \pi G R \rho\right)=\frac{1}{6} g$ Work done in jumping $=m \times g_{m} \times 0.5=m \times\left(\frac{g}{6}\right) m$ $h_{1} =0.5 \times 6=3.0\, m$