Two particles each of mass M and equidistant from each other move along a circle of radius R under the action of their mutual gravitional attraction the speed of each particle is

Options

A. `sqrt(GM)/(2 R)`
B. `(1)/(2R)sqrt(1)/(GM)`
C. `1/2sqrt(GM/R )`
D. `sqrt(4GM)/(R )`

Answer

C

Explanation

Two particles A and B each of mass m move in a circular path of radius R
Then gravitational force between them provides the necessary centripetal force
`(mv^(2))/(R )=(GMm)/(2R)^(2) rarr v=1/2sqrt(GM)/(R )`