Physics - Gravitation Question with Solution | TestHub

The time period of a satellite revolving close to the surface of a planet is given by $T=2\pi \sqrt{\frac{R^3}{GM}}$.

The mass of the planet can be expressed in terms of its mean density $\rho$ and radius $R$ as $M=\frac{4}{3}\pi R^3\rho$.

Substituting the value of $M$ in the expression for $T$:

$T=2\pi \sqrt{\frac{R^3}{G\left(\frac{4}{3}\pi R^3\rho \right)}}$

$T=2\pi \sqrt{\frac{3}{4\pi G\rho }}$

$T=\sqrt{\frac{4{\pi }^2\times 3}{4\pi G\rho }}$

$T=\sqrt{\frac{3\pi }{\rho G}}$

Answer: $\sqrt{\frac{3\pi }{\rho G}}$