$A$ cylindrical vessel partially filled with water is rotated about its vertical central axis. Its surface will

An air bubble of volume $V_0$ is released by a fish at a depth $h$ in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure $P$ above the lake. The volume of the bubble just before touching the surface will be (density of water is $\rho$):

When an air bubble rises from the bottom of a lake to the surface,its radius is doubled. The atmospheric pressure is equal to that of a column of water of height $H$. The depth of the lake is:

$A$ liquid drop of density $\rho$ is floating half-immersed in a liquid of density $d$. If $T$ is the surface tension,then the diameter of the liquid drop is ($g$ = acceleration due to gravity).

When an air bubble of radius $r$ rises from the bottom to the surface of a lake,its radius becomes $\frac{5r}{4}$. Taking the atmospheric pressure to be equal to $10 \ m$ height of water column,the depth of the lake would approximately be ....... $m$ (ignore the surface tension and the effect of temperature).

$A$ tank with a square base of area $1.0 \; m^{2}$ is divided by a vertical partition in the middle. The bottom of the partition has a small hinged door of area $20 \; cm^{2}$. The tank is filled with water in one compartment and an acid (of relative density $1.7$) in the other,both to a height of $4.0 \; m$. Compute the force (in $N$) necessary to keep the door closed.