Two long parallel glass plates have water bet | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The air-water interface between two parallel plates forms a cylindrical meniscus. For a cylindrical surface,the excess pressure $\Delta P$ is give

Vedclass · Accepted Answer

$P_0 - \frac{2T}{d}$

Vedclass · Answer

(D) The air-water interface between two parallel plates forms a cylindrical meniscus. For a cylindrical surface,the excess pressure $\Delta P$ is given by $\Delta P = \frac{T}{R}$,where $R$ is the radius of curvature of the meniscus. Since the contact angle is zero,the meniscus is a semi-cylinder with diameter $d$. Thus,the radius of curvature $R = d/2$. The excess pressure is $\Delta P = P_{atm} - P_{inside} = \frac{T}{R}$. Substituting $R = d/2$,we get $\Delta P = \frac{T}{d/2} = \frac{2T}{d}$. Since the meniscus is concave towards the air,the pressure inside the water is less than the atmospheric pressure. Therefore,$P_{inside} = P_0 - \Delta P = P_0 - \frac{2T}{d}$.

Similar Questions

In a cylinder provided with a piston, air is under pressure $P_1$ at a constant temperature $t$. $A$ soap bubble with radius $r$ and surface tension $T$ is lying inside the cylinder. To reduce the radius of the soap bubble to half, the required air pressure inside the cylinder is

$Assertion :$ $A$ bubble comes from the bottom of a lake to the top.
$Reason :$ Its radius increases.

$27$ drops of mercury coalesce to form a bigger drop. What is the relative increase in surface energy?

$A$ capillary tube of radius $r$ is dipped in a liquid of density $\rho$ and surface tension $S$. If the angle of contact is $\theta$,what is the pressure difference between the two surfaces in the beaker and the capillary?

Two mercury droplets of radii $0.1 \ cm$ and $0.2 \ cm$ coalesce into one single drop. What amount of energy is released? The surface tension of mercury is $T = 435.5 \times 10^{-3} \ N \ m^{-1}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module