Q135 / 160 · AP EAMCET 2022 (06 Jul Shift 2) · Physics

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 Figure

  • A
    $0.4 x$
  • Correct answer
    B
    $0.16 x$
  • C
    $0.8 x$
  • D
    $025 x$

Solution

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

Hence, the correct answer is option: 'B'.

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