Two particles of equal mass move in a circle of radius r under the action of their mutual gravitational attraction. Find the speed of each particle it its mass is m.

Two particles of equal mass move in a circle of radius r under the act

1.	Two particles of equal mass move in a circle of radius r under the action of their mutual gravitational attraction. Find the speed of each particle it its mass is m.
Answer» Solution : The particle will always remain diametrically opposite, so that the force on each particle will be directed along the radius. When each particle is describing a circular orbit, the GRAVITATIONAL force on one of the particles MUST be equal to the necessary centripetal force. `(mV^(2))/(r) = (Gm m)/((2r)^(2)) ""` i.e, `V = sqrt((Gm)/(4r))`