Find the position of the centre of two unequal antiparallel forces. The distance between the points of application of the forces `F_(1)` and `F_(2)` is a.

Answer

`d=F_(2)a//(F_(1)-F_(2))`

Explanation

Resolve the greater force `F_(1)` into two parallel components (Fig.), applying the force `T_(2)= -F_(2)` at the point `A_(2)` and the second force `T_(1)` of magnitude `T_(1)=F_(1)-F_(2)` at the point C at a distance

`d=a T_(2)//T_(1)` from point `A_(1)`. Since the forces `F_(2)` and `T_(2)` are in equilibrium, the resultant `R=T_(1)`, its magnitude is `R=T_(1)=F_(1)-F_(2)`.