$A$ motor is used to deliver water at a certain rate through a given horizontal pipe. To deliver $n$-times the water through the same pipe in the same time, the power of the motor must be increased as follows:

Liquid and gas both are fluids; distinguish between them and state which property is common between them.

Given below are two statements:
Statement $I$: When the speed of a liquid is zero everywhere,the pressure difference at any two points depends on the equation $P_1-P_2=\rho g(h_2-h_1)$.
Statement $II$: In the venturi tube shown,$2gh=v_2^2-v_1^2$.
In the light of the above statements,choose the most appropriate answer from the options given below.

Two cylindrical vessels of equal cross-sectional area $16\,cm^{2}$ contain water up to heights $100\,cm$ and $150\,cm$ respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process is $......J$. [Take density of water $= 10^{3}\,kg/m^{3}$ and $g = 10\,m/s^{2}$]

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