Two long parallel glass plates has water between them. Contact angle between glass and water is zero. If separation between the plates is $'d'$ ( $d$ is small). Surface tension of water is $'T'$ . Atmospheric pressure = $P_0$ . Then pressure inside water just below the air water interface is 

Two soap bubbles coalesce to form a single bubble. If $V$ is the subsequent change in volume of contained air and $S$ change in total surface area, $T$ is the surface tension and $P$ atmospheric pressure, then which of the following relation is correct?

A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by

If a section of soap bubble (of radius $R$) through its center is considered, then force on one half due to surface tension is

When an air bubble of radius $r$ rises from the bottom to the surface of a lake, its radius becomes $\frac{{5r}}{4}$.Taking the atmospheric pressure to be equal to $10\,m$ height of water column, the depth of the lake would approximately be ....... $m$ (ignore the surface tension and the effect of temperature)

A long cylindrical glass vessel has a small hole of radius $'r'$ at its bottom. The depth to which the vessel can be lowered vertically in the deep water bath (surface tension $T$) without any water entering inside is