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Mechanical Properties of Fluids — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsMechanical Properties of Fluids3 Marks
Question
In a hydraulic lift, the input piston has surface area $20 \mathrm{~cm}^2$. The output piston has surface area $1000 \mathrm{~cm}^2$. If a force of $50 \mathrm{~N}$ is applied to the input piston, it raises the output piston by $2 \mathrm{~m}$. Calculate the weight of the support on the output piston and the work done by it.
✓

Answer


$
\begin{aligned}
& \text { Data: } A_1=20 \mathrm{~cm}^2=2 \times 10^{-3} \mathrm{~m}^2, \\
& A_2=1000 \mathrm{~cm}^2=10^{-1} \mathrm{~m}^2, F_1=50 \mathrm{~N}, \mathrm{~s}_2=2 \mathrm{~m}
\end{aligned}
$
(i) By Pascal's law,
$
\begin{aligned}
& \frac{F_1}{A_1}=\frac{F_2}{A_2} \\
& \therefore F_2=F_1 \frac{A_2}{A_1} \\
& =(50 \mathrm{~N}) \times \frac{10^{-1} \mathrm{~m}^2}{2 \times 10^{-3} \mathrm{~m}^2}=50 \times 50 \\
& =2500 \mathrm{~N} \\
&
\end{aligned}
$
This gives the weight of the support on the output piston.
(ii) The work done by the force transmitted to the output piston is
$
\begin{aligned}
& \mathrm{F}_2 \mathrm{~S}_2=(2500 \mathrm{~N})(2 \mathrm{~m}) \\
& =5000 \mathrm{~J}
\end{aligned}
$

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