Q0 4 particles each of mass m are at the corner of a square of side a calculate the net gravitational force acting on any mass due to other three.

Consider square ABCD.

4 particles of mass 'm' are placed at A, B, C and D.

Consider the gracitational forces by masses kept atA, D and C on the mass kept at B.

Force on mass kept at B due to mass kept at A= Gm2/a2

Force on mass kept at B due to mass kept at C= Gm2/a2

Force on mass kept at B due to mass kept at D=Gm2/2a2(as distance between masses=length of diagonal of square=a(root2))

Resultant Force at B= Gm2/a2(root2)

Resultant Force at B and force at B due to C are in same direction.

Hence, Net resultant force=Gm2/a2(root2) + Gm2/2a2

Therefore net resultant force= Gm2/2a2(2(root2) + 1).