Question

Escape velocity from a planet is $ V_{e}$ . If its mass is increased to $8$ times and its radius is increased to $2$ times, then the new escape velocity would be:

• A. $V_{e}$
• B. $ \sqrt{2}v_{e}$
• C. $ 2v_{e}$
• D. $ 2\sqrt{2}v_{e}$

Answer 1

Answer: (C)

Velocity of projection of body, at which the body goes out or gravitational field of earth or planet and never return, is called escape velocity. $v_{e}=\sqrt{\frac{2 G M}{R}}$
where $G$ is gravitational constant, $M$ is mass of plant and $R_{e}$ is radius.
When $M=8\, M,\, R=2 R$,
then $v_{e}=\sqrt{\frac{2 G(8 M)}{(2 R)}} v_{e}=2 \sqrt{\frac{2 G M}{R}}$ $v_{e}=2 v_{e} .$
Note: Escape velocity is independent of mass of body.