An automobile back is lifted by a hydraulic jack that consists of two pistons. The large piston is 70 cm in diameter and the small piston is 8 cm in dimater. If W is the weight of the car, how much smaller a force is required on the small piston in order to lift the car ?

Answer

1.3 % the weight of car

Explanation

Here,`R_1 = 35 cm = 0.35 m , R_1 = 4 cm = 0.4 m`
`F_2 = W, F_1 = ?`
As ` (F_1)/(pi R_1^2) = (F_2)/(pi R_2^2)`
or `F_1 = F_2((R_1)/(R_2))^2 = W((0.04)/(0.035)) = W xx 0.013`
% force required w.r.t weight of car `= (F_1)/(W) xx 100`
`=(0.013W)/(W) xx 100 = 1.3%`