Q. If $\rho$ is the density of the planet, the time period of nearby satellite is given by
A) $\sqrt{\frac{4\pi}{3G\rho}}$
B) $\sqrt{\frac{4\pi}{G\rho}}$
C) $\sqrt{\frac{3\pi}{G\rho}}$
D) $\sqrt{\frac{\pi}{G\rho}}$
Explanation
(c) Time period of nearby satellite
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T = 2n\sqrt{\frac{r^{3}}{GM}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 2\pi\ \sqrt{\frac{R^{3}}{GM}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{2\pi{(R}^{3})^{1/2}}{\left\lbrack G\ \frac{4}{3}\pi R^{3}\rho \right\rbrack^{1/2}} = \sqrt{\frac{3\pi}{G\rho}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.