Two narrow bores of diameter $5.0\, {mm}$ and $8.0\, {mm}$ are joined together to form a $U-$shaped tube open at both ends. If this ${U}$-tube contains water, what is the difference in the level of two limbs of the tube.

[Take surface tension of water ${T}=7.3 \times 10^{-2} \, {Nm}^{-1}$, angle of contact $=0, {g}=10\, {ms}^{-2}$ and density of water $\left.=1.0 \times 10^{3} \,{kg} \,{m}^{-3}\right]$ (in $mm$)

A capillary tube of radius $r$ is dipped in a liquid of density $\rho$ and surface tension $S$. If the angle of contact is $\theta$, the pressure difference between the two surfaces in the beaker and the capillary

A vertical glass capillary tube of radius $r$ open at both ends contains some water (surface tension $T$ and density $\rho$ ). If $L$ be the length of the water column, then:

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

Two soap bubbles of radii $3r$ and $4r$ in contact with each other. The radius of curvature of the interface between bubbles is

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 $....Pa \left( g =10\,ms ^{-2}\right)$