A cylinder of mass m and material density rho | vedclass

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(D) When the cylinder is immersed in the liquid, it displaces a volume of liquid equal to its own volume $V$. According to Archimedes' principle, the

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$\frac{m \sigma g}{\rho A}$

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(D) When the cylinder is immersed in the liquid, it displaces a volume of liquid equal to its own volume $V$. According to Archimedes' principle, the buoyant force $F_B$ exerted by the liquid on the cylinder is $F_B = V \sigma g$. By Newton's third law, the cylinder exerts an equal and opposite force on the liquid, which increases the pressure at the bottom of the vessel. The volume of the cylinder is $V = \frac{m}{\rho}$. The increase in pressure $\Delta P$ is given by the force exerted on the liquid divided by the cross-sectional area $A$ of the vessel: $\Delta P = \frac{F_B}{A} = \frac{V \sigma g}{A}$. Substituting $V = \frac{m}{\rho}$ into the equation: $\Delta P = \frac{(m/\rho) \sigma g}{A} = \frac{m \sigma g}{\rho A}$.

$A$ cylinder of mass $m$ and material density $\rho$ hanging from a string is lowered into a vessel of cross-sectional area $A$ containing a liquid of density $\sigma$ $(< \rho)$ until it is fully immersed. The increase in pressure at the bottom of the vessel is

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