Question

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. $ 3v/4 $
• B. $ 6v $
• C. $ 12v $
• D. $ 3v/2 $

Answer 1

Answer: (B)

Orbital velocity of satellite $ v=\sqrt{\frac{GM}{r}} $ $ \Rightarrow $ $ \frac{{{v}_{A}}}{{{v}_{B}}}=\sqrt{\frac{{{r}_{B}}}{{{r}_{A}}}}=\sqrt{\frac{R}{4R}}=\frac{1}{2} $ $ \therefore $ $ \frac{{{v}_{A}}}{{{v}_{B}}}=\frac{3v}{{{v}_{B}}}=\frac{1}{2} $ $ \therefore $ $ {{v}_{B}}=6v $