Physics - Fluid Question with Solution | TestHub

The height of capillary rise is given by $h=\frac{2T\cos \theta }{r\rho g}$.

For a given liquid and capillary tube, $\frac{h}{\cos \theta }=\text{constant}$.

Initially, the angle of contact is $\theta =0^{\circ }$, so $\cos \theta =1$.

When the tube is depressed, the liquid does not overflow but the meniscus adjusts its shape. The new height of the liquid column is $h^{\prime }=\frac{h}{3}$.

Let the new apparent angle of contact be ${\theta }^{\prime }$.

Using the relation $\frac{h}{\cos \theta }=\frac{h^{\prime }}{\cos {\theta }^{\prime }}$, we get:

$\frac{h}{1}=\frac{\frac{h}{3}}{\cos {\theta }^{\prime }}$

$\cos {\theta }^{\prime }=\frac{1}{3}$

${\theta }^{\prime }={\cos }^{-1}\left(\frac{1}{3}\right)$

Answer: ${\cos }^{-1}\left(\frac{1}{3}\right)$