MHT CET · Physics · Gravitation
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 \(\sqrt{\mathrm{GMm}}\)
- D \(\sqrt{\mathrm{GMm}^2 \mathrm{r}}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{\mathrm{GMm}^2 \mathrm{r}}\)
Step-by-step Solution
Detailed explanation
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,
\(\mathrm{L}=\mathrm{mvr}=\sqrt{\mathrm{GMm}^2 \mathrm{r}}\)
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,
\(\mathrm{L}=\mathrm{mvr}=\sqrt{\mathrm{GMm}^2 \mathrm{r}}\)
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