Three equal masses m are placed at the three corners of an equilateral triangle of side α. Find the force exerted by the system on another particle of mass m placed at
(a) The mid-point of a side,

(b) At the Centre of the triangle.

Question

Philoid · Accepted Answer

(a)From the figure, the forces exerted by particles O and Q are equal and opposite. Hence, only particle P is exerting a force on A.

Distance between particle P and A is

Therefore, the force is given by

(b) At the midpoint (B), the gravitational forces from the particles are equally balanced in all directions. Hence, the total force is zero.

Three equal masses m are placed at the three corners of an equilateral triangle of side α. Find the force exerted by the system on another particle of mass m placed at(a) The mid-point of a side,(b) At the Centre of the triangle.