$A$ pump motor is used to deliver water at a certain rate from a given pipe. To obtain twice as much water from the same pipe in the same time, the power of the motor has to be increased to: (in $\times$)

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

$A$ cylindrical tank of height $1 \ m$ and cross-sectional area $A = 4000 \ cm^2$ is initially empty. It is kept under a tap of cross-sectional area $a_1 = 1 \ cm^2$. Water starts flowing from the tap at $t = 0$ with a speed $v_1 = 2 \ m/s$. There is a small hole in the base of the tank of cross-sectional area $a_2 = 0.5 \ cm^2$. The variation of the height of water in the tank (in meters) with time $t$ is best depicted by:

$27$ equal small water drops combine to form a big drop. If the surface tension of water is $T$ and the radius of a small drop is $r$,then:
$(A)$ The excess pressure inside the big drop is three times the excess pressure inside the small drop.
$(B)$ Surface energy decreases in this process.
$(C)$ In this process,$72 \pi r^2 T$ energy is released.
$(D)$ The radius of the big drop is $3r$.
The true statements are:

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 $P$)

Fill in the blanks:
$(i)$ The lines of flow and streamlines coincide with each other in ...... flow.
$(ii)$ The formula for the horizontal velocity of water coming from a hole at the bottom at a height $h$ from the surface of the water is ......
$(iii)$ $1 \ Pa = ...... \ dyne/cm^{2}$
$(iv)$ The relative velocity of two parallel layers of water is $6 \ cm/s$. If the perpendicular distance between the two layers is $0.1 \ mm$,then the velocity gradient will be ......