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

Question

Escape velocity from a planet is Ve . If its mass is increased to 8 times and its radius is increased to 2 times, then the new escape velocity would be: (A) Ve (B)  √2ve (C)  2ve (D)  2√2ve

Tardigrade Admin · Accepted Answer

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} = \frac{2 GM}{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} = \frac{2 G ( 8 M )}{( 2 R )} v_{e} = 2 \frac{2 GM}{R}

v_{e} = 2 v_{e} .

Note: Escape velocity is independent of mass of body.

Q. 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:

$V_{e}$

$2 v_{e}$

$2 v_{e}$

$22 v_{e}$

Q. Escape velocity from a planet is Ve​ . If its mass is increased to 8 times and its radius is increased to 2 times, then the new escape velocity would be:

Ve​

2​ve​

2ve​

22​ve​

Q. 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:

$V_{e}$

$2 v_{e}$

$2 v_{e}$

$22 v_{e}$