Question

Three particles at the vertices of an equilateral triangle move towards each other....find the initial acceleration of the particles

Answer 1

Three particles at the vertices of an equilateral triangle move towards each other.

velocity magnitude of the particles remains the same throughout the motion ,velocity of each particle would have its component $V Cos 30°$ towards the center and $V Sin30°$ perpendicular to it. Distance of the centre from its vertex at the beginning is $S$ $Cos30°×\large\frac{2}{3}=\sqrt{\frac{S}{3}}$ The component $VSin30°=\large\frac{V}{2}$ is forms tangential component on the circular path described by each particle. Thus the initial centripetal acceleration is

$a=\large\frac{{}{}(V Sin 30°)^2}{r}=\frac{\sqrt{V}}{\sqrt{\frac{S}{3}}} …………. (Since \space r = \sqrt{\frac{S}{3}}) =(V^2)×\frac{\sqrt{3}}{4S}$