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

Fill in the Blank :

$(i)$ Bubble in water have .......... free surface.

$(ii)$ Bubble in air have .......... free surface.

$(iii)$ Rain drop have .......... free surface.

What is the excess pressure inside a bubble of soap solution of radius $5.00 \;mm$, given that the surface tension of soap solution at the temperature ($20\,^{\circ} C$) is $2.50 \times 10^{-2}\; N m ^{-1}$ ? If an air bubble of the same dimension were formed at depth of $40.0 \;cm$ inside a container containing the soap solution (of relative density $1.20$), what would be the pressure inside the bubble? ($1$ atmospheric pressure is $1.01 \times 10^{5} \;Pa$ ).

Formation of bubble are in Column - $\mathrm{I}$ and pressure difference between them are given in Column - $\mathrm{II}$. Match them appropriately.

A container, whose bottom has round holes with diameter $0.1$ $mm $ is filled with water. The maximum height in cm upto which water can be filled without leakage will be ........ $cm$

Surface tension $= 75 \times 10^{-3}$ $ N/m $  and $g = 10$ $ m/s^2$:

If pressure at half the depth of a lake is equal to $2/3$ pressure at the bottom of the lake then what is the depth of the lake...... $m$