Calculate, the gravitational field at point O due to three masses`m_(1),m_(2) and m_(3)` whose positions are given by the following figure. If the masses `m_(1) and m_(2)` are equal what is the change in gravitational field at the point O?

Explanation

Gravitational field due to `m_(1)` at a point .O . is `vec(E)_(1) = (Gm_(1))/(a^(2)) hat(i)`
Gravitational field due to `.m_(1)` at a point .O. is `vec(E)_(2) = - (Gm_(2))/(a^(2)) hat(i)`
(Negative sign indicates field acting along negative x direction )
Gravitational field due to `m_(3` at a point . O . is `vec(E)_(3) = (Gm_(3))/(a^(2)) hat(j)`
`vec(E) = vec(E)_(1)+vec(E)_(2) +vec(E)_(3) = (Gm_(1))/(a^(2))hat(i)- (Gm_(2))/(a^(2)) hat(i) +(Gm_(3))/(a^(2)) hat(j)`
`vec(E) = G/(a^(2)) [ (m_(1)-m_(2))hat(i) +m_(3)hat(j) ] `
If the masses `m_(1) =m_(2) , ` then
`vec(E) = (Gm_(3))/(a^(2)) hat(j)`