The movable cylindrical pistons $P_1$ and $P_2$ of a hydraulic lift are of radii $2 \mathrm{~m}$ and $R$ respectively. A body of mass $32 \mathrm{~kg}$ on piston $P_2$ is supported by a body of mass $2 \mathrm{~kg}$ placed on piston $P_1$. The value of $R$ is

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Aicharya · Accepted Answer

The pistons $P_1$ and $P_2$ of a hydraulic lift are shown below

Using Pascal's law, pressures at piston $P_1$ and $P_2$ will be equal $\begin{array}{ll}\Rightarrow & \frac{F_1}{A_1}=\frac{F_2}{A_2} \\ \Rightarrow & \frac{32 \times g}{\pi R^2}=\frac{2 \times g}{\pi\left(2^2\right.}\end{array}$ $\begin{aligned} \Rightarrow & & 32 \times 2 & =R^2 \\ \text { or } & & R & =8 \mathrm{~m}\end{aligned}$

The movable cylindrical pistons $P_1$ and $P_2$ of a hydraulic lift are of radii $2 \mathrm{~m}$ and $R$…

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