Two satellites A and B rotate around a planet's orbit having radii $4 \mathrm{R}$ and $\mathrm{R}$…
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
$12 \mathrm{~V}$
$\frac{3 \mathrm{~V}}{2}$
$\frac{4 \mathrm{~V}}{2}$
$6 \mathrm{~V}$
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 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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