An air bubble rises from the bottom of a lake to the surface. If its radius increases by $200 \%$ and the atmospheric pressure is equal to a water column of height $H$,then the depth of the lake is ..... $H$.

Two identical cylindrical vessels with their bases at the same level each contain a liquid of density $\rho$. The height of the liquid in one vessel is ${h_1}$ and that in the other vessel is ${h_2}$. The area of either base is $A$. The work done by gravity in equalizing the levels when the two vessels are connected 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.

At a speed of .......... $m/s$,the velocity head of water is equal to the pressure head of $40\, cm$ of $Hg$.

$A$ liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is $r$ and the angular velocity of rotation is $\omega$,then the difference in the heights of the liquid at the centre of the vessel and the edge is

An air bubble of volume $1\,cm^3$ rises from the bottom of a lake $40\,m$ deep to the surface at a temperature of $12^{\circ}C$. The atmospheric pressure is $1 \times 10^5\,Pa$,the density of water is $1000\,kg/m^3$,and $g = 10\,m/s^2$. There is no difference in the temperature of water at the depth of $40\,m$ and on the surface. The volume of the air bubble when it reaches the surface will be $..........\,cm^3$. (in $,cm^3$)