Question

The escape velocity of an object on a planet whose radius is 4 times that of the earth and $g$ value 9 times that on the earth, in kms${}^{-1}$ is

• A. 33.6
• B. 67.2
• C. 16.8
• D. 25.2

Answer 1

The correct option is B 67.2

Escape speed is given by, $v_{min}=\sqrt{2gR}$
which is equal to $\approx 11.2$ km/s on Earth's surface.
For another planet with radius 4 times and $g$ value 9 times that of Earth
$v_{min}^{{}^{\prime }}=\sqrt{2\times 9g\times 4R}$

$=6\times \sqrt{2gR}=6\times 11.2$

$=67.2$ $km/s$