$A$ massless inextensible string in the form of a loop is placed on a horizontal film of soap solution of surface tension $T$. If the film is pierced inside the loop and it converts into a circular loop of diameter $d$,then the tension produced in the string is ..........

Consider a spherical drop of radius $R$. The surface tension of the liquid is $\sigma$. The force of surface tension on the shaded sub-hemisphere due to the remaining drop is $0.5\,\pi \sigma R$. The value of the angle $\theta$ (angle subtended by the sub-hemisphere at the center of the drop) is ......$^o$.

Consider a water tank shown in the figure. It has one wall at $x=L$ and can be taken to be very wide in the $z$ direction. When filled with a liquid of surface tension $S$ and density $\rho$,the liquid surface makes an angle $\theta_0 \left(\theta_0 \ll 1\right)$ with the $x$-axis at $x=L$. If $y(x)$ is the height of the surface,then the equation for $y(x)$ is:
(Take $\theta(x) \approx \sin \theta(x) \approx \tan \theta(x) = \frac{dy}{dx}$,where $g$ is the acceleration due to gravity.)

Write two units of surface tension and give the dimensional formula of surface tension.

$A$ metal wire of density $\rho$ floats on the water surface horizontally. If it is not to sink in water,then the maximum radius of the wire is ($T$ = surface tension of water,$g$ = gravitational acceleration).

The surface tension of a liquid at its boiling point