The property of surface tension is obtained in

$A$ 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).

On heating water,bubbles formed at the bottom of the vessel detach and rise. Assume the bubbles are spheres of radius $R$ and make a circular contact of radius $r$ with the bottom of the vessel. If $r << R$ and the surface tension of water is $T$,find the value of $r$ just before the bubbles detach. (Density of water is $\rho_{w}$)

$A$ 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 ..........

$A$ wire of length $20 \ cm$ is placed horizontally on the surface of water and is gently pulled up with a force of $1.456 \times 10^{-2} \ N$ to keep the wire in equilibrium. The surface tension of water is (in $N \ m^{-1}$)

Detergents are added to water for removing dirt from clothes. Explain.