Q. Three or two planets. The ratio of radius of the two planets is $K$ but ratio of acceleration due to gravity of both planets is $g$. What will be the ratio of their escape velocity?
A) ${(Kg)}^{1/2}$
B) ${(Kg)}^{- 1/2}$
C) ${(Kg)}^{2}$
D) ${(Kg)}^{- 2}$
Explanation
(a) Escape velocity $v = \sqrt{2gR}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{v_{1}}{v_{2}} = \sqrt{\frac{g_{1}}{g_{2}} \times \frac{R_{1}}{R_{2}}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \sqrt{g \times K} = {(Kg)}^{1/2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.