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 three vessels

Answer 1

The correct option is D Same in all the three vessels

Pressure at the bottom of the vessel is given by,

$P=P_0+\rho gh$

Here, $\text{Volume}V=Ah$

$\Rightarrow P=P_0+\frac{\rho gV}{A}$

As, $\rho =\frac{m}{V}$

$\Rightarrow P=P_0+\frac{mg}{A}$

It is clear from the above equation, that pressure at the bottom is independent of density and height of the liquid column.

As, $m$ and $A$ is same for all the three cases,

Pressure at the bottom will be the same in all the three vessels.

Force, $F=PA$

As, $P$ and $A$ are same in all three cases,

Force exerted on the base of all the three vessels will be the same.

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