Question

An artificial sateline moving in a circular orbit around the earth has total energy E (kinetic energy+ potential energy ) . Its potential energy is given by

• A. 2E
• B. $\frac{E}{2}$
• C. $\frac{E}{4}$
• D. Data insufficient

Answer 1

The correct option is A 2E

Total energy of the system $E$ = potential energy $U$ + kinetic energy$KE$

Potential energy of satellite, $U=\frac{-GMm}{r}$

Kinetic energy of satellite,

$KE=\frac{m{v}^2}{2}$

$KE=\frac{m}{2}\left(\frac{GM}{r}\right)\because v=\sqrt{\frac{GM}{r}}$

Total energy,

$E=\frac{-GMm}{r}+\frac{GMm}{2r}$

$E=\frac{-GMm}{2r}$

$E=\frac{1}{2}U$

$U=2E$