Question

Consider the barometer shown in figure. Density of mercury is $\rho$. A small hole is made at point $S$ as shown. The mercury comes out from this hole with speed $v$ equal to:

• A. $\sqrt{2gh}$
• B. $\sqrt{2gH}$
• C. $\sqrt{2g(H-h)}$
• D. None of the above

Answer 1

The correct option is D None of the above

The pressure outside the hole is equal to the atmospheric pressure say $P_o$. The pressure inside the hole $S$ is equal to $P_o-\rho gh$ (where $h$ is the height of the hole above the reservoir level). Since the outer pressure is greater than inside, the mercury will not come out of the hole.