MHT CET · Physics · Gravitation
Two satellites A and B rotate around a planet's orbit having radii \(4 \mathrm{R}\) and \(\mathrm{R}\) respectively. If the speed of satellite \(\mathrm{A}\) is \(3 \mathrm{~V}\) then the speed of satellite B is
- A \(12 \mathrm{~V}\)
- B \(\frac{3 \mathrm{~V}}{2}\)
- C \(\frac{4 \mathrm{~V}}{2}\)
- D \(6 \mathrm{~V}\)
Answer & Solution
Correct Answer
(D) \(6 \mathrm{~V}\)
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 speed can be obtained as:
\(\mathrm{v}=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}}\)
So, \(\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}=6 \mathrm{~V}\), which is the orbital speed of the satellite B.
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 speed can be obtained as:
\(\mathrm{v}=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}}\)
So, \(\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}=6 \mathrm{~V}\), which is the orbital speed of the satellite B.
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