Two particles of equal mass m move around a circle of radius R under the influence of their mutual gravitational attraction, the speed of each particle with respect to their center of mass will be ..........

Options

A. `sqrt((Gm)/(R))`
B. `sqrt((Gm)/(4R))`
C. `sqrt((Gm)/(3R))`
D. `sqrt((Gm)/(2R))`

Answer

B

Explanation

`implies` Centripetal force of any one particle = Gravitational force between two particles .

`mv^2 /R = (GMm)/((2R)^2)`
`(mv^2)/R =(GMm)/(4R_e^2)`
`:. v_2^2 =(GM)/(4R)`
`:.v = sqrt((GM)/(4R))`