Question

Two satellites $A$ and $B$ go round a planet $P$ in circular orbits having radii $4R \, $ and $R$ respectively. If the speed of satellite $A$ is $3V$ , the speed of the satellite $B$ will be.

• A. $12V$
• B. $6V$
• C. $\frac{4}{3} V$
• D. $\frac{3}{2} V$

Answer 1

Answer: (B)

$v = \sqrt{\frac{G M}{R}}$ $\Rightarrow $ $\frac{v_{A}}{v_{B}} = \sqrt{\frac{R_{B}}{R_{A}}} = \sqrt{\frac{R}{4 R}}$ $= \frac{1}{2}$
$\therefore \frac{v_{A}}{v_{B}} = \frac{3 V}{v_{B}} = \frac{1}{2}$
$\therefore \, \, v_{B} = 6 \, V$