The human heart discharges $75 \ cc$ of blood per beat against a pressure of $10 \ cm$ of $Hg$. If the heart beats $72$ times per minute,calculate the power of the heart in $W$. (Given: density of $Hg = 13.6 \ g/cc$ and $g = 9.8 \ m/s^2$)

The vessel shown in the figure has two sections. The lower part is a rectangular vessel with area of cross-section $A$ and height $h$. The upper part is a conical vessel of height $h$ with base area $A$ and top area $a$,and the walls of the vessel are inclined at an angle $30^o$ with the vertical. $A$ liquid of density $\rho$ fills both the sections up to a height $2h$. Neglecting atmospheric pressure:

Given below are two statements:
$Statement$ $(I)$: Viscosity of gases is greater than that of liquids.
$Statement$ $(II)$: Surface tension of a liquid decreases due to the presence of insoluble impurities.
In the light of the above statements,choose the most appropriate answer from the options given below:

The shown $H$-shaped apparatus contains an ideal incompressible liquid and has dimensions as shown in the figure. The diameters of the tubes are small compared to $h$ and $R$. The apparatus is rotated with a constant angular velocity $\omega$ about a symmetric vertical axis as shown in the figure. The pressure at point $A$ is

Drops of liquid of density $d$ are floating half immersed in a liquid of density $\rho$. If the surface tension of the liquid is $T$, then the radius of the drop is

An air bubble of volume $50\, cm^3$ is formed at the bottom of a lake $47.6\, m$ deep. What will be its volume when it reaches the surface? (Atmospheric pressure $= 70\, cm$ of $Hg$ and density of $Hg = 13.6\, g/cm^3$)