To lift a load of 30 kgf, Suhas uses a single fixed pulley while Radha uses a single movable pulley. The displacement of efforts in both the cases are equal. In an ideal situation calculate the ratio of :
the efficiencies in the two cases.
Topic: Efficiency of ideal machines
Answer
Both pulleys are stated to be ideal.
For an ideal machine there is no friction and no weight in the moving parts, so no energy is wasted: efficiency, η = (MA ÷ VR) × 100 %
Fixed pulley: MA = 1, VR = 1 → η = (1 ÷ 1) × 100 = 100 %
Movable pulley: MA = 2, VR = 2 → η = (2 ÷ 2) × 100 = 100 %
Ratio of the efficiencies = 100 : 100 = 1 : 1
Both are ideal, so both are 100 % efficient and the ratio is 1 : 1. The word "ideal" in the question is what settles it.
It is tempting to answer 2 : 1 because that was the answer to the two previous parts, but efficiency and mechanical advantage are different things. A movable pulley gives you twice the force advantage, yet it wastes no more and no less energy than a fixed one when both are ideal — the MA and the VR rise together, so their ratio stays at 1.
In the real world both would fall below 100 %, and the movable pulley would usually be the less efficient of the two, because its effort must also lift the weight of the moving pulley block itself.