$A$ 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 a deep water bath (surface tension $T$) without any water entering inside is

What is the pressure inside the drop of mercury of radius $3.00 \; mm$ at room temperature? Surface tension of mercury at that temperature $(20 \; ^{\circ}C)$ is $4.65 \times 10^{-1} \; N m^{-1}$. The atmospheric pressure is $1.01 \times 10^{5} \; Pa$. Also,calculate the excess pressure inside the drop.

Two soap bubbles having radii $r_1$ and $r_2$ have inside pressures $P_1$ and $P_2$ respectively. If $P_0$ is the external pressure,then the ratio of their volumes is:

An air bubble of radius $0.1\, cm$ is in a liquid having surface tension $0.06\, N/m$ and density $10^3\, kg/m^3$. The pressure inside the bubble is $1100\, N/m^2$ greater than the atmospheric pressure. At what depth $h$ (in $m$) is the bubble below the surface of the liquid? $(g = 9.8\, m/s^2)$

One end of a uniform glass capillary tube of radius $r = 0.025 \ cm$ is immersed vertically in water to a depth $h = 1 \ cm$. The excess pressure in $N/m^2$ required to blow an air bubble out of the tube is: (Surface tension of water $T = 7 \times 10^{-2} \ N/m$,Density of water $\rho = 10^3 \ kg/m^3$,Acceleration due to gravity $g = 10 \ m/s^2$)

$A$ soap bubble of radius $1.0 \text{ cm}$ is formed inside another soap bubble of radius $2.0 \text{ cm}$. The radius of another soap bubble which has the same pressure difference as that between the inside of the smaller and outside of the large soap bubble, in metres is: