Two soap bubbles of radii $r_1$ and $r_2$ coalesce in vacuum under isothermal conditions to form a bigger bubble of radius $R$. What is the radius of the bigger bubble?

An air bubble doubles its radius on rising from the bottom of a water reservoir to the surface. If the atmospheric pressure is equal to $10 \, m$ of water,the height of the water in the reservoir is ..... $m$.

Two small drops of mercury,each of radius $R$,coalesce to form a single large drop. The ratio of the total surface energies before and after the change is:

In air,a charged soap bubble of radius $R$ breaks into $64$ small soap bubbles of equal radius $r$. The ratio of mechanical force per unit area of the big soap bubble to that of a small bubble is

$A$ soap bubble of radius $1.0 \text{ cm}$ is formed inside another soap bubble of radius $2.0 \text{ cm}$. The radius of another soap bubble which has the same pressure difference as that between the inside of the smaller and outside of the large soap bubble, in metres is:

When $n$ identical mercury drops combine to form a single big drop,