In a hydraulic lift, the surface area of the input piston is 6 and that of the output piston is 1500 . If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is ______ kJ. [2025]

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Solution

Q.
In a hydraulic lift, the surface area of the input piston is 6 ${cm}^{2}$ and that of the output piston is 1500 ${cm}^{2}$ . If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is ______ kJ. [2025]

Ans.
(5)

$\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}}, \frac{100}{6} = \frac{F}{1500}, F = \frac{50}{3} \times 1500$

$F = 50 \times 500 = 25 \times 10^{3} N$

$W = \vec{F} . \vec{S} = 25 \times 10^{3} \times \frac{20}{100} = 5 \times 10^{3} = 5 kJ$

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