Question

Three particles each of mass m rotate in a circle of radius r with uniform angular speed $\varpi$ under their mutual gravitational force. If at any instant the points are on the vertex of an equilateral triangle of side L. Then calculate angular speed of each particles.

Answer 1

We have,

$\begin{array}{c}F=\frac{G{m}^2}{l^2}\\ \therefore Fnet=\frac{\sqrt{3}G{m}^2}{l^2}\\ m{w}^{2}e=\frac{\sqrt{3}G{m}^2}{l^2}\\ w=\sqrt{\frac{\sqrt{3}GM}{r{L}^2}}\end{array}$