Question

Radius of orbit of satellite of earth is $R$. Its kinetic energy is proportional to:

• A. $ \frac{1}{R} $
• B. $ \frac{1}{\sqrt{R}} $
• C. $R$
• D. $\frac{1}{R^{3 / 2}}$

Answer 1

Answer: (A)

Kinetic energy of the satellite
$K E=\frac{1}{2} m v_{0}^{2} \,\,\,\,....(1)$
Now putting the value of $v_{0}$ is eq. (1), we get
$K E=\frac{1}{2} m\left(\sqrt{\frac{G M}{R}}\right)^{2}$
$=\frac{1}{2} \frac{m G M}{R}$
Hence, $K E \propto \frac{1}{R}$