question_answer

Two particles of equal mass move in a circle of radius r, under the action of their mutual gravitational attraction. If the mass of each particles is m, the speed of each particles is:

A)  \[\sqrt{\frac{Gm}{r}}\]                     

B)  \[\sqrt{\frac{Gm}{2r}}\]

C)  \[\sqrt{\frac{Gm}{4r}}\]                         

D)  \[\sqrt{\frac{2\,Gm}{r}}\]

Correct Answer: B

Solution :

As,         \[\frac{m{{V}^{2}}}{r/2}=\frac{G{{m}^{2}}}{{{r}^{2}}}\] \[\Rightarrow \]               \[V=\sqrt{\frac{Gm}{2r}}\]