The radius of an air bubble at the bottom of a lake is $r$,and it becomes $2r$ when the air bubble rises to the top surface of the lake. If $P \text{ cm}$ of water is the atmospheric pressure,then the depth of the lake is: (in $P$)

Match column-$I$ with column-$II$.

Column-$I$	Column-$II$
$(A)$ Hydraulic lift	$(P)$ Archimedes' principle
$(B)$ Razor blade can be made to float on the surface of water	$(Q)$ Pascal's law
$(C)$ The dam of a reservoir is made thick at the bottom	$(R)$ Surface tension
$(D)$ Ship is floating on the ocean	$(S)$ Pressure

The heart of a man pumps $5 \, \text{litres}$ of blood through the arteries per minute at a pressure of $150 \, \text{mm}$ of mercury. If the density of mercury is $13.6 \times 10^3 \, \text{kg/m}^3$ and $g = 10 \, \text{m/s}^2$, then the power (in $\text{watt}$) is:

$A$ 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 the vessel is $5 \, cm$ and its rotational speed is $2$ rotations per second,then the difference in the heights between the centre and the sides,in $cm$,will be

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 $\rho$):

$A$ beaker filled with water is accelerated at $a \ m/s^2$ in the $+x$ direction. The surface of the water shall make an angle: