3 equal masses m are placed at the 3 corners of an equilateral of side a Find the exerted by - Physics - Gravitation

Question

3 equal masses m are placed at the 3 corners of an equilateral
of side a Find the exerted by the system on anther particle of mass
m placed at (1)the mid point of the side ,(2) at the center of the
tringle

Jyoti Pant · Accepted Answer

(a) At the mid point of sideThe force of attraction of the particle at A on the particle at D is given by,FA=Gm2(32a)2=43Gm2a2 along DAThe force of attraction of the particle at B on the particle at D is given by,FB=Gm2(a/2)2=4Gm2a2 along DBFC=Gm2(a/2)2=4Gm2a2 along DCFB= FC (opposite forces), thus cancel each other Therefore,The resultant force acting on particle at mid point (D) of a side isFR=FA=43Gm2a2

(b) The forces FA,FB and FC acting on particle at the centroid 'D' of triangle are equal i e FA=FB = FC=FThe angle between FB and FC, θ=1200Using parallelgram law of vectors, the resultant of FB and FC is given byF'= FB2+ FC2+2 FBFCcosθ=F2+F2+2F2cos1200=F (along DA)Since the resultant is equal and opposite to FA,Thus, the net force acting on the particle at D is given by,FR=F'-FA=F-F=0 newton

3 equal masses m are placed at the 3 corners of an equilateral of side a.Find the exerted by the system on anther particle of mass m placed at (1)the mid point of the side ,(2) at the center of the tringle