Three particles of identical masses . m . are kept at the vertices of an equilateral triangle of each side length .a. . Find the gravitational force of attraction on any one of the particles.

Three particles of identical masses . m . are kept at the vertices of

1.	Three particles of identical masses . m . are kept at the vertices of an equilateral triangle of each side length .a. . Find the gravitational force of attraction on any one of the particles.
Answer» SOLUTION :Let `F_A and F_B` be the FORCES due to the masses at A and B on the mass at C . Here `F_A = F_B` Hence the Resultant force on the mass at C `F = 2F_A"cos"theta//2 = 2.(Gm^2)/a^2 cos 30^@` `= 2 xx(Gm^2)/a^2xxsqrt3/2 = SQRT3(Gm^2)/a^2`