question_answer

Two satellites A and B go around a planet P in circular orbits having radius 4R and R respectively. If the speed of satellite A is 3v, then the speed of satellite B will be

A)  6 v                                        

B)  9 v

C)  3 v                        

D)         none of these

Correct Answer: A

Solution :

The gravitational force provides the necessary centripetal force, \[\therefore \]  \[F=\frac{GMm}{{{r}^{2}}}=\frac{Mv_{o}^{2}}{r}\] \[\Rightarrow \]               \[{{v}_{o}}=\sqrt{\frac{GM}{r}}\] Given,\[{{v}_{A}}=3v,\,\,{{r}_{A}}=R,\,\,{{r}_{B}}=4R\] \[\therefore \]  \[\frac{3v}{{{v}_{B}}}=\sqrt{\frac{R}{4R}}=\frac{1}{2}\] \[\Rightarrow \]               \[{{v}_{B}}=6\,\,v\]