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.

Explanation

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^(2)) xx (sqrt(3))/(2) -sqrt(3)(Gm^(2))/(a^(2))`