Question

A beaker of circular cross-section of radius $5\text{cm}$ is filled with mercury upto a height of $15\text{cm}$. Find the force exerted by the mercury on the bottom of the beaker. Take atmospheric pressure $={10}^5{\text{N/m}}^2$, density of mercury $=13600{\text{kg/m}}^3$, and $g=10{\text{m/s}}^2$.

• A. $9425\text{N}$
• B. $942.5\text{N}$
• C. $94.25\text{N}$
• D. $785.4\text{N}$

Answer 1

The correct option is B $942.5\text{N}$

Atmospheric pressure, $P_o={10}^5{\text{N/m}}^2$
The pressure at the bottom,
$P=P_o+\rho gh$
$\Rightarrow P={10}^5+13600\times 10\times 0.15$
$\Rightarrow P=1.2\times {10}^5{\text{N/m}}^2$
$\therefore$ The force exerted by the mercury on the bottom is
$F=PA$
$\Rightarrow F=1.2\times {10}^5\times \pi \times (0.05{)}^2$
$\Rightarrow F=942.5\text{N}$