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Two satellites $$A$$ and $$B$$ go round a planet in circular orbits having radii $$4R$$ and $$R$$ respectively. If the speed of $$A$$ is $$3v$$, the speed of $$B$$ will be :
Two satellites A and B with orbital radii 4R and R. Speed of A = 3v. Find speed of B.
For a circular orbit, the orbital speed formula is $$v = \sqrt{\frac{GM}{r}}$$, so $$v \propto \frac{1}{\sqrt{r}}$$.
Using this relation, $$\frac{v_B}{v_A}=\sqrt{\frac{r_A}{r_B}}=\sqrt{\frac{4R}{R}}=2$$ and hence $$v_B=2v_A=2\times3v=6v$$.
The correct answer is Option (2): 6v.
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