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 ..... $m$.

$A$ 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......$cm$.

$27$ drops of mercury coalesce to form a bigger drop. What is the relative increase in surface energy?

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

Two soap bubbles, $A$ and $B$, have radii in the ratio $3 : 2$. The ratio of the excess pressure inside bubble $A$ to that of bubble $B$ is:

The excess pressure inside a soap bubble is $1.5$ times the excess pressure inside a second soap bubble. The volume of the second bubble is '$x$' times the volume of the first bubble. The value of '$x$' is