Question

If the mean radius of eaith is R, its angular velocity is $\omega$ and the, acceleration due to gravity at the surface of the earth is 'g' thien the, cube of the radius of the orbit of a satellite will be

• A. $\frac{Rg}{{\omega }^2}$
• B. $\frac{R^{2}g}{\omega }$
• C. $\frac{R^{2}g}{{\omega }^2}$
• D. $\frac{R^{\omega }}{g}$

Answer 1

Answer: (C)

Time period of satellite,
$T=\frac{2\pi r^{3/2}}{\sqrt{GM}}$ or $\sqrt{GM}=\frac{2\pi }{T}\cdot r^{3/2}$
$<br/>\frac{2\pi }{T}=\omega <br/>$
$\therefore \omega r^{3/2}=\sqrt{GM}$ or $r^3=\frac{GM}{{\omega }^2}=\frac{g{R}^2}{{\omega }^2}$