The movable cylindrical pistons P_1 and P_2 o | vedclass

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(A) According to Pascal's law, the pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of

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(A) According to Pascal's law, the pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel. Therefore, the pressure at both pistons $P_1$ and $P_2$ must be equal.Let $F_1$ and $F_2$ be the forces applied on pistons $P_1$ and $P_2$ respectively, and $A_1$ and $A_2$ be their respective areas.$F_1 = m_1 g = 2g$$F_2 = m_2 g = 32g$$A_1 = \pi (2)^2 = 4\pi$$A_2 = \pi R^2$Equating the pressures: $\frac{F_1}{A_1} = \frac{F_2}{A_2}$$\frac{2g}{4\pi} = \frac{32g}{\pi R^2}$$\frac{1}{2} = \frac{32}{R^2}$$R^2 = 64$$R = 8 \,m$

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

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