A hydraulic lift is shown in the figure. The radii of the movable pistons $P_1$ and $P_2$ are $2 \mathrm{~m}$ and $5 \mathrm{~m}$ respectively. If a block of mass $x$ is placed on $P_2$ then the minimum mass that should be kept on $P_1$ to lift the block on $P_2$ is

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Aicharya · Accepted Answer

Given $r_1=2 \mathrm{~m}, r_2=5 \mathrm{~m}$ According to Pascal's law $ \begin{aligned} p_1 & =p_2 \ \frac{F_1}{A_1} & =\frac{F_2}{A_2} \ \Rightarrow \quad \frac{m_1 g}{\pi r_1^2} & =\frac{m_2 g}{\pi r_2^2} \end{aligned} $ $\begin{array}{rlrl}\Rightarrow & & \frac{m_1}{r_1^2} & =\frac{m_2}{r_2^2} \ \Rightarrow & \frac{m_1}{2^2} & =\frac{x}{5^2} \ \Rightarrow & & m_1 & =\frac{4}{25} x \ & & =0.16 x\end{array}$

A hydraulic lift is shown in the figure. The radii of the movable pistons $P_1$ and $P_2$ are $2…

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