JAMB Physics 2019 Paper

Concept:A screw jack converts a small turning effort at the handle into a large lifting force. Efficiency relates mechanical advantage to velocity ratio.Explanation:Given pitch $P = 0.45\, \text{cm}$ and arm length $L = 60\, \text{cm}$.For one complete turn, the effort moves a circle of radius $L$, so the distance moved is $2\pi L$.The velocity ratio of the screw jack is:$$VR = \frac{2\pi L}{P} = \frac{2\pi \times 60}{0.45} = \frac{120\pi}{0.45} = \frac{800\pi}{3}$$Efficiency is given as $\frac{75}{\pi}\%$.Using efficiency formula:$$\text{Efficiency} = \frac{MA}{VR} \times 100\%$$So:$$\frac{75}{\pi} = \frac{MA}{\frac{800\pi}{3}} \times 100$$Simplifies to:$$MA = \frac{\frac{75}{\pi}}{100} \times \frac{800\pi}{3} = \frac{75 \times 800}{100 \times 3} = 200$$Answer:Mechanical advantage $= 200$, which is option C.