Three equal masses m are placed at the three corners of an equilateral triangle of side a. find the force exerted by this system on another particle of mass m placed at (a) the mid point of a side (b) at the center of the triangle.

Answer

A, B, C, D

Explanation

a. If m is palced at mid point of a side then `vecF_(OA)=(4Gm^2)/a^2` in OA direction
`vecF_(OB)=(4Gm^2)/a^2` in OB direction
Since equal and opposite forces cancel each other `vecF_(OC)=(4Gm^2)/({(3)a^2})`
`=(4Gm^2)/(3a^2)` in OC direction
b. If placed at 0 (centroid)
Resultant `vecF_(OA)+vecF_(OB)+vecF_(OC)=0`
(because fore are equal and opposite)
Net gravitatioN/Al force =0