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 the another single soap bubble of radius $r\,cm$. The value of $r$ is.......

A $U-$ tube with limbs of diameters $5\, mm$ and $2\, mm$ contains water of surface  tension $7 \times 10^{-2}$ newton per metre, angle of contact is zero and density $10^3\, kg/m^3$. If $g$ is $10 \,m/s^2$, then the difference in level of two limbs is :-

The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be $75\, cm$ of $Hg$ and the density of water to be $1/10  $ of the density of mercury, the depth of the lake is ....... $m$

If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is $R$ and surface tension of water is $T$ then the pressure in water between the plates is lower by

Two soap bubbles of radii $2 \,cm$ and $4 \,cm$ join to form a double bubble in air, then radius of curvature of interface is .......... $cm$

There is an air bubble of radius $1.0\,mm$ in a liquid of surface tension $0.075\,Nm ^{-1}$ and density $1000\,kg$ $m ^{-3}$ at a depth of $10\,cm$ below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is $....Pa \left( g =10\,ms ^{-2}\right)$