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In a hydraulic lift, used at a service station the radius of the large and small piston are in the ratio of \( 20: 1 . \) What weight placed on the small piston will be sufficient to lift a car of mass 1500 kg?

1. \( 3.75 \mathrm{kg} \)
2. 37.5 kgg \( g \)
3. \( 7.5 \mathrm{kg} \)
4. 75 kg

Correct answer: 37.5 kgg \( g \)

Solution

In a hydraulic lift, the pressure transmitted through the fluid is equal, so force is proportional to piston area. Since area scales as radius squared, a 20:1 radius ratio gives a 400:1 area ratio, making the needed small-piston force 1500/400 of the car’s weight.

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