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 potential energy gained by the loads in the two cases.
Topic: Velocity ratio and load displacement
Answer
The effort displacement is the same in both cases; call it d.
The velocity ratio tells you how far the load rises:
fixed pulley, VR = 1 → load rises d ÷ 1 = d
movable pulley, VR = 2 → load rises d ÷ 2 = d/2
The load is the same, 30 kgf, in both cases, so the potential energy gained is proportional to the height risen: PE = load × height
Suhas : Radha = (30 × d) : (30 × d/2) = d : d/2 = 2 : 1
Ratio of the potential energy gained by the loads = 2 : 1
The condition "the displacement of efforts in both cases are equal" is what makes the question work. With the same effort distance, the fixed pulley raises its load the full distance while the movable pulley raises its load only half as far.
Same load, half the height, so half the potential energy gained. Notice this does NOT contradict part (a): Radha pulls with half the force over the same distance, so she does half the work and her load gains half the energy. Energy in equals energy out in both cases — that is exactly what makes them both 100 % efficient.
The movable pulley makes the pulling easier, not the job smaller. To raise her load as high as Suhas raises his, Radha would have to pull twice as far.