G L Mittal and TARUN MITTAL Solutions for Chapter: Surface Tension, Exercise 2: NUMERICALS

(a) The radius of a capillary tube is $0.025 \mathrm{mm}$. It is held vertically in a liquid whose density is $0.8\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$,surface tension is $3.0\times {10}^{-2} \mathrm{N} {\mathrm{m}}^{-1}$ and for which the cosine of the angle of contact is $0.3$. Determine the height up to which the liquid will rise in the tube. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$
(b) If the capillary is taken down in water slowly until its upper end comes in level of water, will the water come out from this end ?

Water rises in a capillary tube to a height of $5.0 \mathrm{cm}$ If surface tension of water is $9.8\times {10}^{-2} \mathrm{N} {\mathrm{m}}^{-1}$, then find out the diameter of the capillary tube.

The radius of a capillary tube is $0.8 \mathrm{mm}$ and the water rises in it up to a height of $2 \mathrm{cm}$. Calculate the surface tension of water. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

A liquid rises to a height of $7.0 \mathrm{cm}$ in a capillary tube of radius $0.1 \mathrm{mm}$. The density of the liquid is $0.8\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. If the angle of contact between the liquid and the surface of the tube be zero, calculate the surface tension of the liquid. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

Water rises up in a glass capillary up to a height of $9.0 \mathrm{cm}$,,$ while mercury falls down by $3.4 \mathrm{cm}$ in the same capillary. Assume angles of contact for water-glass and mercury-glass $0°$ and $135°$ respectively. Determine the ratio of surface tensions of mercury and water $\left(\cos 135°=-0.71\right)$

Water rises up to $2.0 \mathrm{cm}$ in a capillary tube of length $20.0 \mathrm{cm}$ held vertically. If the capillary is bent by $30°$ from this vertical position, find the length of liquid risen in it.

A capillary tube of the radius $0.4 \mathrm{mm}$ is dipped vertically in the water. Find up to what height the water will rise in the capillary. If the capillary is inclined at an angle of $60°$ with the vertical, how much length of the capillary is occupied by water? The surface tension of water is $7.0\times {10}^{-2}{\mathrm{Nm}}^{-1}$.

Water rises in a capillary up to a height of $8.0 \mathrm{cm}$. If the capillary is inclined at an angle of $45°$ with the vertical, then determine the vertical height of water. How much length of the capillary will be occupied by water? If the length of the capillary is reduced to $4.0 \mathrm{cm}$ and it is held vertically in the water, then what will be the position of water?