Question

Three particles each of mass M are located at the vertices of an equilateral triangle of side 'a'. At what speed must they move if they all revolve under the influence of their gravitational force of attraction in a circular orbit circumscribing the triangle while still preserving the triangle.

Answer 1

The radius of the circle is a3

The net gravitational force acting on any particle

F=Gm2a2cos300+cos300=3Gm2a2

This force must be equal to the centripetal force on the particle. so,

3Gm2a2=mv2a3⇒v2=Gma⇒v=Gma

So the speed of the particle is Gma

Answer 2

Answer:

speed of the system must be GMa