Question

In a two step pulley arrangement meant for a load W, the ratio between force P and W in equilibrium position when radii of pulleys are r₁ and r₂

• A. $\frac{r_{2}}{r_{1} - r_{2}}$
• B. $\frac{r_{1} - r_{2}}{r_{2}}$
• C. $\frac{r_{1}}{r_{1} - r_{1}}$
• D. $\frac{r_{2} - r_{1}}{r_{1}}$

Answer 1

Answer: (A)

$\frac{r_{2}}{r_{1} - r_{2}}$

Answer 2

Let the pulley be given a small rotation θ in anticlockwise direction, the pulley and load will be lifted by r₂θ and P moves down by (r₁θ - r₂θ).

Equating virtual work done to zero

P(r₁θ - r₂θ) – Wr₂θ = 0

or $\frac{P}{W} = \frac{r_{2}}{r_{1} - r_{2}}$