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

When a mercury drop of radius $R$ breaks into $n$ droplets of equal size,the radius $r$ of each droplet is

$A$ soap bubble,having a radius of $1\; mm$,is blown from a detergent solution having a surface tension of $2.5 \times 10^{-2}\; N/m$. The pressure inside the bubble is equal to the pressure at a point $Z_{0}$ below the free surface of water in a container. Taking $g=10\; m/s^{2}$ and the density of water $\rho = 10^{3}\; kg/m^{3}$,the value of $Z_{0}$ is......$cm$.

When two small bubbles join to form a bigger one,energy is

$A$ spherical soap bubble of radius $3\,cm$ is formed inside another spherical soap bubble of radius $6\,cm$. If the internal pressure of the smaller bubble of radius $3\,cm$ in the above system is equal to the internal pressure of another single soap bubble of radius $r\,cm$,then the value of $r$ is:

Two small drops of liquid of same radius coalesce to form a big drop. The ratio of the total surface energies after and before the change is