Gravitation Ques 44
44. The radii of circular orbits of two satellites $A$ and 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:
[2010]
(a) $3 V / 4$
(b) $6 $ $V$
(c) $12 $ $V$
(d) $3 V / 2$
Show Answer
Answer:
Correct Answer: 44.(b)
Solution:
- (b) Orbital velocity of a satellite in a circular orbit of radius a is given by
$ \begin{aligned} & v=\sqrt{\frac{G M}{a}} \\ & \Rightarrow v \propto \sqrt{\frac{1}{a}} \\ & \Rightarrow \frac{v_2}{v_1}=\sqrt{\frac{a_1}{a_2}} \\ & \therefore v_2=v_1 \sqrt{\frac{4 R}{R}}=2 v_1=6 V \end{aligned} $
BETA
