Gravitation - Result Question 45
48. The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively. If the speed of satellite $A$ is $3 V$, then the speed of satellite $B$ will be:
(a) $3 V / 4$
(b) $6 V$
(c) $12 V$
(d) $3 V / 2$
[2010]
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Answer:
Correct Answer: 48. (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} $
