Practicing Success
A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity $\frac{3\pi}{Gd}$ represents |
$\sqrt{T}$ $T$ $T^2$ $T^3$ |
$T^2$ |
Time Period of revolution of satellite is $ T = 2\pi \sqrt {\frac{R^3}{GM}} $ $ \text{If d is the density then } M = \frac{4\pi}{3} R^3 d$ $\Rightarrow T = 2\pi \sqrt {\frac{R^3}{Gd\frac{4\pi}{3} R^3}}= 2\pi \sqrt{\frac{3}{4\pi Gd}}$ $\Rightarrow T^2 = \frac{3\pi}{Gd}$ |