Q. The ratio of the radii of the planets $P_{1}$ and $P_{2}$ is $a$. The ratio of their acceleration due to gravity is $b$. The ratio of the escape velocities from them will be
A) $ab$
B) $\sqrt{ab}$
C) $\sqrt{a/b}$
D) $\sqrt{b/a}$
Explanation
(b) $\frac{\left( v_{e} \right)p_{1}}{\left( v_{e} \right)p_{2}} = \frac{\sqrt{2g_{1}R_{1}}}{\sqrt{2g_{1}R_{2}}} = \sqrt{\frac{g_{1}}{g_{2}} \times \frac{R_{1}}{R_{2}}} = \sqrt{ab}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.