Three particles each of mass 'm' rotate in a circle of radius 'r' with a constant angular velocity 'ω', due to their mutual gravitational attraction. At a certain time, the particles occupy a position on the circular path as if they are on the vertex of an equilateral triangle. If each side of the equilateral triangle is 'a', then
1
\(\omega =\sqrt{\frac{{3Gm}}{a^3}}\)
2
\(\omega =\frac{\sqrt{Gm}}{a^3}\)
3
\(\omega =\sqrt{\frac{{2Gm}}{3a^3}}\)
4
\(\omega =\frac{\sqrt{Gm}}{3a^3}\)