The rate of diffusion is

$A$ bubble of radius $R$ in water of density $\rho$ is expanding uniformly at speed $v$. Given that water is incompressible,the kinetic energy of water being pushed is

The figure shows a three-arm tube in which a liquid is filled up to a height $l$. It is now rotated at an angular frequency $\omega$ about an axis passing through arm $B$. Find the angular frequency $\omega$ at which the level of liquid in arm $B$ becomes zero.

Two cylindrical vessels of equal cross-sectional area $16\,cm^{2}$ contain water up to heights $100\,cm$ and $150\,cm$ respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process is $......J$. [Take density of water $= 10^{3}\,kg/m^{3}$ and $g = 10\,m/s^{2}$]

An air bubble rises from the bottom of a water tank of height $5 \ m$. If the initial volume of the bubble is $3 \ mm^3$,what will be its volume as it reaches the surface (in $mm^3$)? Assume that its temperature does not change. $[g=9.8 \ m \ s^{-2}, 1 \ atm=10^5 \ Pa, \text{density of water}=1 \ g/cm^3]$

$A$ horizontal fire hose with a nozzle of cross-sectional area $\frac{5}{\sqrt{21}} \times 10^{-3} \text{ m}^2$ delivers a cubic metre of water in $10 \text{ s}$. What will be the maximum possible increase in the temperature of water while it hits a rigid wall (neglecting the effect of gravity) (in $^{\circ} \text{C}$)?