Given below are two statements :
Statement I: A satellite is moving around earth in the orbit very

Question

Given below are two statements : 
Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.
Statement II: The time period of revolution of the satellite is $T=2 \pi \sqrt{\frac{R_e}{g}}$ (for satellite very close to the earth surface), where $R_{\mathrm{e}}$ radius of earth and $g$ acceleration due to gravity.
In the light of the above statements, choose the correct answer from the options given below :

Professor PC Thomas Classes · Answer

The time period of a satellite very close to the Earth's surface is $T = 2\pi\sqrt{\frac{R_e}{g}}$, making Statement II true. Since $g = \frac{GM}{R_e^2}$ and mass $M = \frac{4}{3}\pi R_e^3 \rho$, we have $g = \frac{4}{3}\pi G R_e \rho$. Substituting this into the time period formula gives $T = 2\pi\sqrt{\frac{R_e}{\frac{4}{3}\pi G R_e \rho}} = \sqrt{\frac{3\pi}{G\rho}}$. This shows that the time period depends solely on the density $\rho$ of the Earth, making Statement I true as well.