Q. The ratio of the radius of a planet $'A'$ to that of planet $'B'$ is $'r'$. The ratio of acceleration due to gravity on the planets is $'x'$. The ratio of the escape velocities from the two planets is
A) $xr$
B) $\sqrt{\frac{r}{x}}$
C) $\sqrt{rx}$
D) $\sqrt{\frac{x}{r}}$
Explanation
(c) $v_{e} = \sqrt{2gR} \Rightarrow \frac{v_{A}}{v_{B}} = \sqrt{\frac{g_{A}}{g_{B}} \times \frac{R_{A}}{R_{B}}} = \sqrt{x \times r}\therefore\frac{v_{A}}{v_{B}} = \sqrt{rx}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.