Question

Escape velocity at surface of earth is $11.2\,km/s$. 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

The Correct Option is 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
$v_{e}=\sqrt{\frac{2 G M_{e}}{R_{e}}}$
Given, $M_{e}=M_{p}, R_{p}=\frac{R_{e}}{4}$
$\therefore \frac{v_{p}}{v_{e}}=\sqrt{\frac{M_{e}}{M_{e}} \times \frac{R_{e}}{R_{e / 4}}}$
$=\sqrt{4}=2$
$\Rightarrow v_{p}=2 v_{e}=2 \times 11.2$
$=22.4 \,km / s$