Question

Consider the barometer shown in figure. If a small hole is made at point $A$ in the barometer tube, then

• A. Mercury will come out from this hole after $10\text{sec}$
• B. Mercury will not come out from this hole
• C. First, mercury will come out and then stop after $10\text{sec}$
• D. Mercury will come out from this hole after $15\text{sec}$

Answer 1

The correct option is B Mercury will not come out from this hole

We know that flow of fluid takes place when there is difference in pressure and the flow occurs from high pressure region to low pressure region.


$P_C=P_B=\rho g{h}_0$ (hydrostatic pressure due to height of liquid).
Hence, atmospheric pressure:
$P_0=P_C=P_B=\rho g{h}_0...\left(1\right)$
and hydrostatic pressure due to depth of liquid above $A$ is,
$P_A=0+\rho gh=\rho gh...\left(2\right)$
We can see from figure
$h_0>h$
From Eq.$\left(1\right)$ and $\left(2\right)$, $P_0>P_A$


As atmospheric pressure on the fluid at point $A$ is greater than the fluid pressure due to depth, mercury will not come out of the hole.