Question

If the period of revolution of an artificial satellite just above the earth's surface is T and the density of earth is $\rho$, then $\rho T^2$ is

• A. A universal constant whose value is $\frac{3\pi }{G}$
• B. A universal constant whose value is $\frac{3\pi }{2G}$
• C. Proportional to radius of earth R
• D. Proportional to square of the radius of earth $R^2$ Here, G= universal gravitational constant

Answer 1

The correct option is A

A universal constant whose value is $\frac{3\pi }{G}$

Here, G = universal gravitation constant

Time period of a satellite above the earth's surface is :

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

or $\rho T^2=\frac{3\pi }{G}$ = a universal constant.