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The radii of circular orbits of two satellites A and $B$ of the earth are $4 R$ and $R$, respectively. If the speed of satellite $A$ is $3 v$, then the speed of satellite $B$ will be
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The correct answer is:
$6 v$
$$
\begin{aligned}
& \text { Orbital velocity of satellite } \mathrm{v}=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}} \\
& \begin{array}{ll}
\Rightarrow & \frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}=\sqrt{\frac{\mathrm{r}_{\mathrm{B}}}{\mathrm{r}_{\mathrm{A}}}}=\sqrt{\frac{\mathrm{R}}{4 \mathrm{R}}}=\frac{1}{2} \\
\therefore & \frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}=\frac{3 \mathrm{v}}{\mathrm{v}_{\mathrm{B}}}=\frac{1}{2} \\
\therefore & \mathrm{v}_{\mathrm{B}}=6 \mathrm{v}
\end{array}
\end{aligned}
$$
\begin{aligned}
& \text { Orbital velocity of satellite } \mathrm{v}=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}} \\
& \begin{array}{ll}
\Rightarrow & \frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}=\sqrt{\frac{\mathrm{r}_{\mathrm{B}}}{\mathrm{r}_{\mathrm{A}}}}=\sqrt{\frac{\mathrm{R}}{4 \mathrm{R}}}=\frac{1}{2} \\
\therefore & \frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}=\frac{3 \mathrm{v}}{\mathrm{v}_{\mathrm{B}}}=\frac{1}{2} \\
\therefore & \mathrm{v}_{\mathrm{B}}=6 \mathrm{v}
\end{array}
\end{aligned}
$$
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