The radii of circular orbits of two satellites A and $B$ of the earth are $4 R$ and $R$, respectively. If…

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
  1. $3 y / 4$
  2. $6 v$
  3. $12 y$
  4. $3 v / 2$

Solution

$\begin{aligned} & \text { Orbital velocity of satellite } \mathrm{v}=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}} \\ & \begin{array}{ll} \Rightarrow & \frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}=\sqrt{\frac{\mathrm{r}_{\mathrm{B}}}{\mathrm{r}_{\mathrm{A}}}}=\sqrt{\frac{\mathrm{R}}{4 \mathrm{R}}}=\frac{1}{2} \\ \therefore & \frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}=\frac{3 \mathrm{v}}{\mathrm{v}_{\mathrm{B}}}=\frac{1}{2} \\ \therefore & \mathrm{v}_{\mathrm{B}}=6 \mathrm{v} \end{array} \end{aligned}$ .

Asked in: NEET 2010 (Screening)

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