QJEEAdv23Ph6688: JEE Advanced 2023 Physics - Class 11 JEEAdv23Ph6688 Solution: An incompressible liquid is kept in a container having a…

An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius $0.1 \mathrm{~mm}$ is dipped vertically into the liquid through the airtight piston hole, as shown in the figure. The air in the container is isothermally compressed from its original volume $V_0$ to $\frac{100}{101} V_0$ with the movable piston. Considering air as an ideal gas, the height $(h)$ of the liquid column in the capillary above the liquid level in $\mathrm{cm}$ is _______.

[Given: Surface tension of the liquid is $0.075 \mathrm{~N} \mathrm{~m}^{-1}$ , atmospheric pressure is $10^5 \mathrm{~N} \mathrm{~m}^{-2}$ , acceleration due to gravity $(\mathrm{g})$ is $10 \mathrm{~m} \mathrm{~s}^{-2}$ , density of the liquid is $10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ and contact angle of capillary surface with the liquid is zero]