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 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 vessels.

Answer 1

The correct option is D same in all the vessels.

Let $m$ be mass of the liquid. Let $h_A,h_B$ and $h_C$ be the heights of liquid level in the three vessels. Then

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

${\rho }_A{h}_A={\rho }_B{h}_B={\rho }_C{h}_C=\frac{m}{A}$

Pressure at the bottom in vessel $A$, $P_A=P_0+{\rho }_{A}g{h}_A$

Similarly, at $B$ and $C,$
$P_B=P_0+{\rho }_{B}g{h}_B$
$P_C=P_0+{\rho }_{C}g{h}_C$

i.e., $P_A=P_B=P_C$

So, the same force will be exerted by the liquids in all the
three vessels.