JAMB Physics 2018 Paper

Concept:A block-and-tackle pulley system transfers effort into load. Its efficiency is found by comparing the mechanical advantage with the velocity ratio.Explanation:The diagram shows six rope segments supporting the movable pulley block, so the velocity ratio is $V.R = 6$.The load is $120.0\,\mathrm{N}$, and the efficiency is given as $40\%$.Use the efficiency formula:$\text{Efficiency} = \frac{\text{M.A}}{V.R} \times 100$Substitute the values:$40 = \frac{\text{M.A}}{6} \times 100$Simplify to find the mechanical advantage:$6 \times 40 = 100 \times \text{M.A}$$\text{M.A} = \frac{240}{100} = 2.4$Mechanical advantage is also:$\text{M.A} = \frac{\text{Load}}{\text{Effort}}$Thus:$2.4 = \frac{120}{W}$Solving for the effort:$W = \frac{120}{2.4} = 50.0\,\mathrm{N}$Answer:The value of $W$ is $50.0\,\mathrm{N}$. The correct option is D.