Embibe Experts Solutions for Chapter: Viscosity and Surface Tension, Exercise 3: Exercise-3

$PQRS$ is a rectangular frame of copper wire shown in figure the side $RS$ of the frame is movable. If a soap film is formed on it then what is the diameter (in $\mathrm{mm}$ ) of the wire to maintain equilibrium (Given surface tension of soap solution $=0.045 \mathrm{N} {\mathrm{m}}^{-1}$ and density of copper $\left.=8.96\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}\right)$

The pressure of air in a soap bubble of $0.7 \mathrm{c}\mathrm{m}$ diameter is $8 \mathrm{m}\mathrm{m}$ of water above the atmospheric pressure. Calculate the surface tension of soap solution. Take $g=9.8 \mathrm{m}{\mathrm{s}}^{-2}$.

The capillary tube is dipped in water vertically. It is sufficiently long so that water rises to maximum height h in the tube. The length of the portion immersed in water is $l>h.$ The lower end of the tube is closed, the tube is taken out and opened again. Then, find the length of the water column (in metre) remaining in the tube. ( given $h=4 \mathrm{m})$

There is a $1 \mathrm{mm}$ thick layer of glycerine between a flat plate of area $100{ \mathrm{cm}}^2$ and a big plate. If the coefficient of viscosity of glycerine is $1.0 \frac{\mathrm{kg}}{\mathrm{m}-\sec },$ then how much force (in $\mathrm{N}$ ) is required to move the plate with a velocity of $7 \frac{\mathrm{cm}}{\sec }.$

A spherical ball of radius $3.0\times {10}^{–4} \mathrm{m}$ and density ${10}^4 \mathrm{kg} {\mathrm{m}}^{-3}$ falls freely under gravity through a distance $h$ before entering a tank of water. If after entering the water the velocity of the ball does not change, find $h$. Viscosity of water is $9.8\times {10}^{–6} \mathrm{N} \mathrm{s} {\mathrm{m}}^{-2}$. $[g= 9.8 \mathrm{m} {\mathrm{s}}^{-2}, {\rho }_w=1000 \mathrm{kg} {\mathrm{m}}^{-3}]$