Two satellites 'A' and 'B' are revolving with critical velocities ' $\mathrm{v}_{\mathrm{A}}$ ' and '…
Two satellites 'A' and 'B' are revolving with critical velocities ' $\mathrm{v}_{\mathrm{A}}$ ' and ' $\mathrm{v}_{\mathrm{B}}$ ' around
the earth, in circular orbits of radii ' $\mathrm{R}$ ' and ' $2 \mathrm{R}^{\prime}$, respectively. The ratio $\frac{\mathrm{V}_{\mathrm{A}}^{\prime}}{\mathrm{V}_{\mathrm{B}}}$ is
$2: 1$
$\sqrt{2}: 1$
$1: 2$
$1: \sqrt{2}$
Solution
Critical velocity of the satellite is given by
$\begin{aligned}
\mathrm{V} &=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}} \\
\therefore \frac{\mathrm{V}_{\mathrm{A}}}{\mathrm{V}_{\mathrm{B}}} &=\sqrt{\frac{2 \mathrm{R}}{\mathrm{R}}}=\sqrt{2}
\end{aligned}$