Question

Equal masses of three liquids are kept in three identical cylindrical vessels $A,B$ and $C$. Their densities are ${\rho }_A,{\rho }_B$ and ${\rho }_C$ with ${\rho }_A<{\rho }_B<{\rho }_C$. The force exerted by the liquid on the base will be,

• A. maximum in vessel $A$
• B. maximum in vessel $B$
• C. maximum in vessel $C$
• D. same in all the three vessels

Answer 1

The correct option is D same in all the three vessels

Let $m$ be mass of the liquid
$h_A,h_B$ and $h_C$ be the heights of liquid level in three vessels respectively.
Now, $\rho =\frac{m}{V}\Rightarrow m=\rho V$

$\therefore m={\rho }_{A}A\times h_A={\rho }_{B}A\times h_B={\rho }_C\times A\times h_C$

$\Rightarrow {\rho }_A{h}_A={\rho }_B{h}_B={\rho }_C{h}_C$ [Vessels are identical]
Pressure at the bottom of the vessel is given by,
$P_A=P_{atm}+{\rho }_{A}g{h}_A$
$P_B=P_{atm}+{\rho }_{B}g{h}_B$
$P_C=P_{atm}+{\rho }_{C}g{h}_C$

$\therefore P_A=P_B=P_C$

i.e. the same force will be exerted by the liquid in all the three vessels.

Hence, $\left(D\right)$ is the correct answer.