Question

in the diagram shown the liquid has density $\rho$ Atmospheric pressure is $P_0$ . The pressure at point A is

• A. $P_0+\frac{\rho gh}{2}$
• B. $P_0-\frac{\rho gh}{2}$
• C. $\frac{\rho gh}{2}$
• D. None of these

Answer 1

The correct option is B $P_0-\frac{\rho gh}{2}$

In capillary we know:-

$P{a}_1=P{a}_2=P{w}_2$

Then,

$P{w}_2=P{w}_1+\rho gh$

$\Rightarrow P{a}_1-P{w}_1=\rho gh$

$\Rightarrow P{w}_1=P{a}_1-\rho gh$

Thus, at height $h/2$ we will have

$P=P{w}_1+\rho g\frac{h}{2}=P{a}_1-\rho gh+\rho g\frac{h}{2}=P{a}_1-\rho g\frac{h}{2}$

$[P{a}_1=P_0]$.