Q. Time speed of revolution of a nearest satellite around a planet of radius $R$ is $T$. Period of revolution around another planet, whose radius is $3R$ but having same density is
A) $T$
B) $3T$
C) $9T$
D) $3\sqrt{3}T$
Explanation
(a) Time period of satellite which is very near to planet
$T = 2\pi\sqrt{\frac{R^{3}}{GM}} = 2\pi\sqrt{\frac{R^{3}}{G\frac{4}{3}\pi R^{3}\rho}}\ \therefore T \propto \sqrt{\frac{1}{\rho}}$
$i.e.$ time period of nearest satellite does not depends upon the radius of planet, it only depends upon the density of the planet.
In the problem, density is same so time period will be same
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.