Four particles of equal mass are moving round a circle of radius r due to their mutual gravitational attraction Find - Physics - Gravitation

Question

Four particles of equal mass are moving round a circle of radius
r due to their mutual gravitational attraction Find the angular
velocity of each particle?

Jyoti Pant · Accepted Answer

The all particles will remain diametrically opposite so that the force on each particle will be directed along the radius
Suppose we consider the motion of one of the particles
The force on the particle is given by,F=Gm24r2If the speed is v, thena=v2rAccording to Newton's law,Gm24r2=mv2rv=GM4rAngular velocity, ω=vr=GM4r×1r=GM4r3

Four particles of equal mass are moving round a circle of radius r due to their mutual gravitational attraction.Find the angular velocity of each particle?