Given below are two statements:
Statement-1: For a satellite orbiting the Earth in a circular orbit, its orbital velocity increases if its orbital radius increases.
Statement-2: The total energy of a satellite orbiting the Earth in a circular orbit is negative and is equal to half of its potential energy.

Question

Given below are two statements:

Statement-1: For a satellite orbiting the Earth in a circular orbit, its orbital velocity increases if its orbital radius increases.

Statement-2: The total energy of a satellite orbiting the Earth in a circular orbit is negative and is equal to half of its potential energy.

TestHub · Accepted Answer

Statement-1: For a satellite in a circular orbit, the orbital velocity is given by $v_{o} = \frac{GM}{r}$ , where $r$ is the orbital radius. As $r$ increases, $v_{o}$ decreases. Thus, Statement-1 is false.

Statement-2: The potential energy of a satellite is $U = - \frac{GM m}{r}$ . The kinetic energy is $K = \frac{1}{2} m v_{o}^{2} = \frac{1}{2} m (\frac{GM}{r}) = \frac{GM m}{2 r}$ . The total energy is $E = K + U = \frac{GM m}{2 r} - \frac{GM m}{r} = - \frac{GM m}{2 r}$ . So, $E = \frac{1}{2} U$ . The total energy is negative and is half of its potential energy. Thus, Statement-2 is true.

Physics - Gravitation Question with Solution | TestHub

Options:

Doubts & Discussion

JEE Main 2027 (Class 12+)