D. C. Pandey Solutions for Chapter: Fluid Mechanics, Exercise 2: Excercise 2

A small spherical droplet of density $d$ is floating exactly half immersed in a liquid of density $\rho$ and surface tension $T$. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet),

A leak proof cylinder of length $1 \mathrm{m}$, made of a metal which has very low coefficient of expansion is floating vertically in water at $0 °\mathrm{C}$ such that its height above the water surface is $20 \mathrm{cm}$. When the temperature of water is increased to $4 °\mathrm{C}$, the height of the cylinder above the water surface becomes $21 \mathrm{cm}$. The density of water at $T=4 °\mathrm{C}$, relative to the density at $T=0 °\mathrm{C}$ is close to

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,

A long cylindrical vessel is half-filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is $5 \mathrm{cm}$ and its rotational speed is $2$ rotations per second, then the difference in the heights between the centre and the sides (in $\mathrm{cm}$ ) will be

Two separate soap bubbles of radii $8\times {10}^{-3} \mathrm{m}$ and $2\times {10}^{-3} \mathrm{m}$ respectively formed of same liquid (surface tension $6.5\times {10}^{-2} \mathrm{N} {\mathrm{m}}^{-1}$ ) come together to form a double. The radius of interlace of double bubble is

A water tank kept on the ground has an orifice of $2 \mathrm{mm}$ diameter on the vertical side. What is the minimum height of the water above the orifice for which the output flow of water is found to be turbulent? (Assume, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, ${\rho }_{\mathrm{water}}={10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$, viscosity $=1 \mathrm{centi}-\mathrm{poise}$)

A copper ball of radius $3.0 \mathrm{mm}$ falls in an oil tank of viscosity $1 \mathrm{kg} {\mathrm{m}}^{-1} {\mathrm{s}}^{-1}$. Then, the terminal velocity of the copper ball will be (Density of oil $=1.5\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$, Density of copper$=9\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ and $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.)

The radius of a soap bubble is $r$ and the surface tension of the soap solution is $S$. The electric potential to which the soap bubble be raised by charging it so that the pressure inside the bubble becomes equal to the pressure outside the bubble is ( ${\epsilon }_0=$ permittivity of the free space)