A uniform rod is kept on a frictionless horizontal table and two forces F 1 and F 2 are…

A uniform rod is kept on a frictionless horizontal table and two forces F₁ and F₂ are acted as shown in figure. The line of action of force \(F_{f_{1}}\) (which produces same torque) is at a perpendicular distance ‘C’ from O. Now F₁ and F₂ are interchanged and F₁ is reversed. The new forces \(F_{R_{2}}\) (which produces torque of same magnitude in the present case) has its line of action at a distance \(\frac{\mathcal{C}}{2}\) from O. If the \(F_{f_{1}}\) : \(F_{R_{2}}\) in the ratio 2:1, then a: b is (assume \(\left.F_{2} a>F_{1} b\right):\)