Four identical masses of m are kept at the corners of a square of side a. Find the gravitational force exerted on one of the masses by the other masses.

Explanation

`F_(12) = (Gm^2)/( a^2)`
`F_13 = (Gm^2)/( 2a^2)`
`F_14 = (Gm^2)/( a^2)`
`F= sqrt(F_12^2 + F_14)+F_13`
`= sqrt(((Gm^2)/( a^2))^2 + ((GM^2)/( a^2))^2)+ (Gm^2)/( a^2)`
`= (Gm^2)/( a^2) sqrt(2) + (Gm^2)/( 2a^2 )`
`F= (Gm^2)/( a^2) [ sqrt(2) + (1)/(2) ]`