Soap solution is used for cleaning dirty clothes because

$A$ metal wire of length $L$ and density $d$ floats horizontally on the free surface of water. What is the maximum radius of the wire such that it does not sink in water? [$T$ = surface tension of water, $g$ = gravitational acceleration]

What is the effect of increasing temperature on surface tension?

$A$ square frame of each side $L$ is dipped in a soap solution and taken out. The force acting on the film formed is ($T$ = surface tension of soap solution). (in $TL$)

$A$ thread is tied slightly loose to a wire frame as shown in the figure. The frame is dipped into a soap solution and taken out,such that the frame is completely covered with a soap film. When the portion $A$ is punctured with a pin,the thread:

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 $\rho_{w}$)