In a cylinder provided with a piston, air is under pressure $P_1$ at a constant temperature $t$. $A$ soap bubble with radius $r$ and surface tension $T$ is lying inside the cylinder. To reduce the radius of the soap bubble to half, the required air pressure inside the cylinder is

If two soap bubbles of different radii are connected by a tube,then

$A$ spherical drop of radius $r$ is divided into $8$ equal droplets. If the surface tension is $S$, then the work done in the process will be

$A$ big drop of radius $R$ is formed by $1000$ small droplets of water. The radius of each small droplet is:

What is the excess pressure inside a bubble of soap solution of radius $5.00 \; mm$,given that the surface tension of soap solution at the temperature $(20 \; ^{\circ}C)$ is $2.50 \times 10^{-2} \; N m^{-1}$? If an air bubble of the same dimension were formed at a depth of $40.0 \; cm$ inside a container containing the soap solution (of relative density $1.20$),what would be the pressure inside the bubble? ($1$ atmospheric pressure is $1.01 \times 10^{5} \; Pa$).

$A$ soap bubble assumes a spherical surface. Which of the following statements is wrong?