Question

The ratio of the radius of the earth to that of the moon is $10$. The ratio of the acceleration due to gravity on the earth to that of the moon is $6$. The ratio of the escape velocity from the earth's surface to that from the moon is

• A. $4$
• B. $\sqrt{60}$
• C. $\sqrt{120}$
• D. None of these

Answer 1

The correct option is B $\sqrt{60}$

Escape velocity from surface of a planet is $v=\sqrt{2gR}$
Ratio of escape velocities on earth and moon is
$\frac{v_e}{v_m}=\sqrt{\frac{g_e}{g_m}\times \frac{R_e}{R_m}}=\sqrt{\frac{6}{1}\times \frac{10}{1}}=\sqrt{60}$