Three equal masses m are located at the three corners of an equilateral triangle of side a . Evaluate the force exerted by this arrangement on an additional particle of mass m placed at the centre of the triangle.

Step-by-step solution

Let the three masses be placed at the vertices A, B, and C of the equilateral triangle, and the additional mass be placed at the centroid O. The gravitational force exerted by the mass at A on the mass at O is F _A directed along OA. Similarly, the forces due to the masses at B and C are F _B and F _C directed along OB and OC respectively. Since the triangle is equilateral, the distances from the centroid to the vertices are equal, i.e., OA = OB = OC . Therefore, the magnitudes of the three forces are equal: | F _A