Two particles of equal masses m go round a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is `v=sqrt((Gm)/(nR))`. Find the value of n.

Options

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

Answer

C

Explanation

Centripetal force provided by the gravitational force of attraction between two particles

i.e. `(mv^(2))/( R) = (GM xx m)/((2 R) ^(2))`
`v = (1)/(2) sqrt((Gm)/( R))`