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\[3\upsilon ,\] then the speed of satellite B will be

A)  6v                                         

B)  9V

C)  3v                                         

D)  None of these

Correct Answer: A

Solution :

                The gravitational force provides the necessary centripetal force \[\therefore \]  \[F=\frac{GMm}{{{r}^{2}}}\]                 \[=\frac{Mv_{0}^{2}}{r}\]                 \[{{v}_{0}}=\sqrt{\frac{GM}{r}}\] Given,   \[{{v}_{A}}=3v,{{r}_{A}}=R,{{r}_{B}}=4R\] \[\therefore \]  \[\frac{3v}{{{v}_{B}}}=\sqrt{\frac{R}{4R}}=\frac{1}{2}\] or            \[{{v}_{B}}=6v\]