Question

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

• A. $\frac{mpg}{\sigma s}$
• B. $\frac{mg}{s}$
• C. $\frac{mg}{\sigma }$
• D. $Zero$

Answer 1

Answer: (A)

$\frac{mpg}{\sigma s}$

When cylinder will immerse in the liquid then Upthrust force will apply on then cylinder and same amount of downward force will act of the liquid by the cyliner.

change in pressure is given by

$\Delta P=\frac{F_u}{s}$

where $F_u$ is upthrust force, puttin values we get

$\Delta P=\frac{V\rho g}{s}$

using $\sigma =\frac{m}{V}$ we get :

$\Delta P=\frac{m\rho g}{\sigma s}$

Hence option A is correct.