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
  1. $2: 1$
  2. $\sqrt{2}: 1$
  3. $1: 2$
  4. $1: \sqrt{2}$

Solution

Critical velocity of the satellite is given by $\begin{aligned} \mathrm{V} &=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}} \\ \therefore \frac{\mathrm{V}_{\mathrm{A}}}{\mathrm{V}_{\mathrm{B}}} &=\sqrt{\frac{2 \mathrm{R}}{\mathrm{R}}}=\sqrt{2} \end{aligned}$

Asked in: MHT CET 2020 (12 Oct Shift 1)

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