$A$ disc of paper of radius $R$ has a hole of radius $r$. It is floating on a liquid of surface tension $T$. The force of surface tension on the disc is

$A$ thin metal disc of radius $r$ floats on the water surface and bends the surface downwards along the perimeter,making an angle $\theta$ with the vertical edge of the disc. If the disc displaces a weight of water $W$ and the surface tension of water is $T$,then the weight of the metal disc is:

When water is heated,bubbles form at the bottom and detach to rise. Let the radius of the bubble be $R$. The bubble is in circular contact with the bottom of the container with a radius $r$. If $r \ll R$ and the surface tension of water is $T$,find the value of $r$ just before the bubble detaches from the container. (Density of water is $\rho_w$)

The length of a needle floating on the surface of water is $1.5\,cm$. The force in addition to its weight required to lift the needle from the water surface will be...... $N$ (surface tension of water $= 7.5\,N/cm$).

$A$ 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:

Air (density $\rho$) is being blown on a soap film (surface tension $T$) by a pipe of radius $R$ with its opening right next to the film. The film is deformed and a bubble detaches from the film when the shape of the deformed surface is a hemisphere. Given that the dynamic pressure on the film due to the air blown at speed $v$ is $\frac{1}{2} \rho v^{2}$,the speed at which the bubble is formed is: