An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius 0.1 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 cm is_______.
[Given: Surface tension of the liquid is 0.075 N m⁻¹ , atmospheric pressure is 10⁵ N m⁻², acceleration due to gravity (g) is 10 m s⁻² , density of the liquid is 10³ kg m⁻³ and contact angle of capillary surface with the liquid is zero]

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answer is 25.

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Detailed Solution

$\begin{array}{l} h = \frac{2 T}{γρg} + \frac{Δp}{ρg} \\ = \frac{2 \times 0.75}{1 \times 10^{- 3} \times 10^{3} \times 10} + \frac{p / 101}{10^{3} \times 10} \\ = \frac{15}{1} + \frac{10^{5}}{101 \times 10^{4}} \\ = . 15 + \frac{10}{100} = . 25 m = 25 cm \end{array}$