Question

The escape velocity for a rocket on the earth is $11.2km/sec$. Its value on a planet where acceleration due to gravity is twice that on the earth and the diameter of the planet is twice that of the earth, will be (in $km/sec$):

• A. $11.2$
• B. $5.6$
• C. $22.4$
• D. $33.6$

Answer 1

Answer: (C)

$22.4$

Answer is B.
The minimum velocity with which a body must be projected up so as to enable it to just overcome the gravitational pull, is known as escape velocity.
If $v_e$ is the required escape velocity, then kinetic energy which should be given to the body is $\frac{1}{2}m{v_e}^2$.
$\frac{1}{2}m{v_e}^2=\frac{GMm}{R}$
$⟹v_e=\sqrt{\frac{2GM}{R}}$
$⟹v_e=\sqrt{2gR}$
In this case, the acceleration due to gravity is twice that on the earth and the diameter of the planet is twice that of the earth.
So, $v_e=\sqrt{2\times 2g\times 2R}=2\sqrt{2gR}$.
Hence, the escape velocity is $11.2km/sec\times 2=22.4$ km/sec.