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 if 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 if 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=(Gmm)/(2r)^2` i.e., `V=sqrt((Gm)/(4r))`