Two particles of equal mass m each , go round a circle of radius R, under the action of their mutual gravitational attraction. The speed of each particle is

Options

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

Answer

C

Explanation

Centripetal force = Gravitational force or `(mv^(2))/(R) = (G m xx m)/((2 R)^(2))`
or `v^(2) = (Gm)/(4 R) or v = (1)/(2) sqrt((Gm)/(R))`