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 $\rho T^{2}$ :

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

Answer 1

Answer: (A)

For a revolving satellite by Kepler's Third Law we use $T^{2}=\left(4 \pi^{2} / G M\right) R^{3}$ and $M=\left(4 \pi R^{3} / 3\right) \rho$ we get option $( A )$ is correct.