Question

Escape velocity at surface of earth is $11.2km/s$. Escape velocity from a planet whose mass is the same as that of earth and radius $1/4$ that of earth, is :

• A. 2.8 km/s
• B. 15.6 km/s
• C. 22.4 km/s
• D. 44.8 km/s

Answer 1

Answer: (C)

At a certain velocity of projection the body will go out of the gravitational field of the earth and will never return of the earth, this velocity is known as escape velocity
$v_e=\sqrt{\frac{2G{M}_e}{R_e}}$
Given, $M_e=M_p,R_p=\frac{R_e}{4}$
$\therefore \frac{v_p}{v_e}=\sqrt{\frac{M_e}{M_e}\times \frac{R_e}{R_{e/4}}}$
$=\sqrt{4}=2$
$\Rightarrow v_p=2v_e=2\times 11.2$
$=22.4km/s$