Q114 / 150 · MHT CET 2022 (05 Aug Shift 1) · Physics
A satellite of mas ' $m$ ' is revolving around the earth of mass ' $M$ ' in an orbit of radius ' $r$ '. The angular momentum of the satellite about the centre of orbit will of
- A$\sqrt{\mathrm{GMmr}}$
- B$\sqrt{\mathrm{Mvr}}$
- C$\sqrt{\mathrm{GMm}}$
- Correct answerD$\sqrt{\mathrm{GMm}^2 \mathrm{r}}$
Solution
The correct option is (D).
Considering force balance in the orbit:
$\frac{\mathrm{GMm}}{\mathrm{r}^2}=\frac{\mathrm{mv}^2}{\mathrm{r}}$
Gravitational force balances the centrifugal force. The orbital velocity can be obtained as:
$v=\sqrt{\frac{G M}{r}}$
Therefore, angular momentum is equal to,
$\mathrm{L}=\mathrm{mvr}=\sqrt{\mathrm{GMm}^2 \mathrm{r}}$
Hence, the correct answer is option: 'D'.