Question

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

• A. zero
• B. $\frac{mg}{A}$
• C. $\frac{mg\rho }{\sigma A}$
• D. $\frac{m\sigma g}{\rho A}$

Answer 1

The correct option is D $\frac{m\sigma g}{\rho A}$

Volume of cylinder $=\frac{m}{\rho }$

Upthrust on cylinder $=(\frac{m}{\rho })\sigma g$

From Newton's third law,thr downward force exerted by cylinder on the liquid is $=(\frac{m}{\rho })\sigma g$

Therefore increase in pressure $=\frac{m\sigma g}{\rho A}$