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Q. For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

JIPMERJIPMER 2008Gravitation

Solution:

Key Idea Kinetic energy of satellite is half of its potential energy.
Potential energy of satellite
$U=-\frac{G M_{e} m}{R_{e}}$
where $R_{e}$ is radius of earth, $M_{e}$ the mass of earth, $m$ the mass of satellite and $G$ the gravitational constant.
$|U|=\frac{G M_{e} m}{R_{e}}$
Kinetic energy of satellite
$K=\frac{1}{2} \frac{G M_{e} m}{R_{e}}$
Thus, $\frac{K}{|U|}=\frac{1}{2} \frac{G M_{e} m}{R_{e}} \times \frac{R_{e}}{G M_{e} m}=\frac{1}{2}$