Question

Three particles, each of the mass `m` are situated at the vertices of an equilateral triangle of side `a`. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original mutual separation `a`. Find the initial velocity that should be given to each particle and also the time period of the circular motion. `(F=(Gm_(1)m_(2))/(r^(2)))`

Answer 1

Correct Answer - A::B::C
`r=a/2 sec 30^(@)=a/(sqrt(3))`
`F=(Gmm)/(a^(2))`
`F_(net)=sqrt(3)F=((Gmm)/(a^(2))) (sqrt(3))`

This will provided the necassary centripetal force.
`:. (mv^(2))/r=(sqrt(3)Gm^(2))`
`T=(2pir)/v=(2pi(a//sqrt(3)))/(sqrt(Gm//a))=2pisqrt((a^(3))/(3Gm))`