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