Two soap bubbles have radii in the ratio of \(2:3\). Compare the excess pressure inside them.
Ans: \(\frac{P_{1}}{P_{2}}=\frac{3}{2}\).
A long cylindrical vessel has a very small hole of radius \(0.5\,mm\) at its bottom. Find: the depth to which the vessel can be lowered vertically in the deep water bath without any water entering into it. Given: Surface tension of the water \(=0.072\frac{N}{m}\), density of water \(=1000\frac{kg}{m^{3}}\) and \(g=9.8\frac{m}{s^{2}}\).
Ans: \(h=2.94\,cm\).
If, the excess pressure inside a soap bubble is balanced by oil column of height \(2\,mm\). Then find: the surface tension of oil. Given: Radius of bubble \(=1\,cm\) and density \(0.8\frac{g}{cm^{3}}\).
Ans: \(\sigma=39.2\frac{dyne}{cm}\).
Calculate: the excess pressure inside a bubble of air of radius \(0.1\,mm\) just below the surface of the water. What would be the pressure inside it if it is at a depth of \(10\,cm\) below the surface of the water. Given: \(g=9.8\frac{m}{s^{2}}\), \(\rho_{water}=1000\frac{kg}{m^{3}}\), \(P_{atm}=\left(1.013\times10^{5}\right)Pa\) and Surface Tension \(=0.0727\frac{N}{m}\).
Ans: \(P=\left(1.0373\times10^{5}\right)Pa\).
The lower end of a capillary tube of diameter \(2.00\,mm\) is dipped \(8.00\,cm\) below the surface of water in a beaker. What is the pressure required in the tube in order to blow a hemispherical bubble at its end in water? The surface tension of the water at the temperature of the experiment is \(\left(7.30\times10^{-2}\right)\frac{N}{m}\), 1 Atmospheric pressure \(=\left(1.01\times10^{5}\right)Pa\), Density of water \(=1000\frac{kg}{m^{3}}\), \(g=9.8\frac{m}{s^{2}}\). Also calculate: the excess of pressure.
Ans: \(P_{tube}=146\,Pa\) and \(P_{excess}=\left(1.02\times10^{5}\right)Pa\).
The excess pressure inside a spherical drop is four times that of another drop of same liquid. Find: the ratio of their respective masses.
Ans: \(1:64\).
Find: the pressure inside an air bubble of radius \(0.01\,mm\) situated at a depth of \(1\,m\) below the surface of water in a pond. Given: Atmospheric Pressure \(=0.76\,m\) of mercury column, Surface tension of water \(=0.072\frac{N}{m}\) and Density of water \(1\frac{g}{cm^{3}}\). Density of mercury \(13600\frac{kg}{m^{3}}\).
