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 ..........

Two particles of equal mass m move around a circle of radius R under t

1.	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 ..........
Answer» `SQRT((Gm)/(R))` `sqrt((Gm)/(4R))` `sqrt((Gm)/(3R))` `sqrt((Gm)/(2R))` Solution :`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))`