Question

The maximum vertical distance through which a fully dressed astronaut can jump on the earth is $0.5m$. If mean density of the Moon is two-third that of the earth and radius is one quarter that of the earth, the maximum vertical distance which he can jump on the Moon and the ratio of the time of duration of the jump on the Moon to hold on the earth are

• A. $6m$, $1:6$
• B. $3m$, $6:1$
• C. $3m$, $1:6$
• D. $6m$, $3:1$

Answer 1

Answer: (B)

The work that the astronaut can do is same on both earth and the moon.

Hence, $m{g}_e{h}_e=m{g}_m{h}_m$

$⟹m\left(\frac{G{M}_e}{R_e^2}\right)h_e=m\left(\frac{G{M}_m}{R_m^2}\right)h_m$

Using $M=\rho \frac{4}{3}\pi R^3$,

$h_m=h_e\left(\frac{{\rho }_e{R}_e}{{\rho }_m{R}_m}\right)=3m$

Again since work done has be to same. initial kinetic energy would same at both the places, hence the initial velocity.

$t_{jump}=\frac{2v_0}{g}$

$⟹\frac{t_m}{t_e}=\frac{{\rho }_e{R}_e}{{\rho }_m{R}_m}=6:1$