Q. The escape velocity for the earth is $v_{e}$. The escape velocity for a planet whose radius is four times and density is nine times that of the earth, is
A) $36v_{e}$
B) $12v_{e}$
C) $6v_{e}$
D) $20v_{e}$
Explanation
(b) $v \propto R\sqrt{\rho}\ \therefore\frac{v_{p}}{v_{e}} = \frac{R_{p}}{R_{e}} \times \sqrt{\frac{\rho_{p}}{\rho_{e}}} = 4 \times \sqrt{9} = 12$
$\Rightarrow v_{p} = 12v_{e}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.