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 $$3v,$$ then the speed of satellite $$B$$ will be
A.
$$\frac{{3v}}{4}$$
B.
$$6v$$
C.
$$12v$$
D.
$$\frac{{3v}}{2}$$
Answer :
$$6v$$
Solution :
Orbital velocity of satellite is given by, $$v = \sqrt {\frac{{GM}}{r}} $$
Ratio of orbital velocities of $$A$$ and $$B$$ is given by,
$$\eqalign{
& \Rightarrow \frac{{{v_A}}}{{{v_B}}} = \sqrt {\frac{{{r_B}}}{{{r_A}}}} = \sqrt {\frac{R}{{4R}}} = \frac{1}{2} \cr
& \therefore \frac{{{v_A}}}{{{v_B}}} = \frac{{3v}}{{{v_B}}} = \frac{1}{2} \cr
& \therefore {v_B} = 6v \cr} $$
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