Question

The mass of earth is $81$ times that of the moon and the radius of the earth is $3.5$ times that of the moon. The ratio of the escape velocity on the surface of earth to that on the surface of moon will be:

• A. $0.2$
• B. $2.57$
• C. $4.81$
• D. $0.39$

Answer 1

The correct option is C $4.81$

Given : $\frac{M_E}{M_M}=81$ and $\frac{R_E}{R_M}=3.5$

Escape velocity $v_e=\sqrt{\frac{2GM}{R}}$

$⟹$ $\frac{v_{e_E}}{v_{e_M}}=\sqrt{\frac{M_E}{M_M}\times \frac{R_M}{R_E}}$

$\frac{v_{e_E}}{v_{e_M}}=\sqrt{81\times \frac{1}{3.5}}=4.81$