$A$ cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The diameter of the vessel is $10 \, cm$ and the angular speed of rotation is $\omega \, rad \, s^{-1}$. The difference in the height,$h$ (in $cm$),of the liquid at the centre of the vessel and at the side will be

An incompressible liquid is kept in a container having a weightless piston with a hole. $A$ capillary tube of inner radius $0.1 \,mm$ is dipped vertically into the liquid through the airtight piston hole,as shown in the figure. The air in the container is isothermally compressed from its original volume $V_0$ to $\frac{100}{101} V_0$ with the movable piston. Considering air as an ideal gas,the height $(h)$ of the liquid column in the capillary above the liquid level in $cm$ is. . . . . . .
[Given: Surface tension of the liquid is $0.075 \,N \,m^{-1}$,atmospheric pressure is $10^5 \,N \,m^{-2}$,acceleration due to gravity $(g)$ is $10 \,m \,s^{-2}$,density of the liquid is $10^3 \,kg \,m^{-3}$ and contact angle of capillary surface with the liquid is zero]

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 $g = 9.8 \ m/s^2$)

Match the columns $I$ and $II$:

Column $I$	Column $II$
$A$. Stoke's law	$I$. Pressure and energy
$B$. Turbulence	$II$. Hydraulic lift
$C$. Bernoulli's Principle	$III$. Viscous drag
$D$. Pascal's law	$IV$. Reynold's number

The correct match is:

Given below are two statements:
Statement $I$: Pressure of fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.
Statement $II$: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension.
In the light of the above statements, choose the correct answer from the options given below.

Two blocks of ice when pressed together join to form one block because