Three identical particles each of mass "m" are arranged at the corners of an equiliteral triangle of side "L". If they are to be in equilibrium, the speed with which they must revolve under the influence of one another's gravity in a circular orbit circumscribing the triangle is

Options

A. `sqrt((3Gm)/L)`
B. `sqrt((Gm)/L)`
C. `sqrt((Gm)/(3L))`
D. `sqrt((3Gm)/(L^(2)))`

Answer

B

Explanation

`sqrt(3)F=(mv^(2))/r, F=(Gm_(1)m_(2))/(L^(2))` and `r=L/(sqrt(3))`