$A$ liquid drop of density $Q$ is floating half-immersed in a liquid of density $d$. What is the diameter of the liquid drop? ($Q$ > $d$, $g = $ acceleration due to gravity, $T = $ surface tension)

$A$ horizontal fire hose with a nozzle of cross-sectional area $\frac{5}{\sqrt{21}} \times 10^{-3} \text{ m}^2$ delivers a cubic metre of water in $10 \text{ s}$. What will be the maximum possible increase in the temperature of water while it hits a rigid wall (neglecting the effect of gravity) (in $^{\circ} \text{C}$)?

Which of the following phenomena is not due to surface tension?

$A$ vertical cylindrical container of base area $A$ and an upper cross-section area $A_1$ making an angle $30^{\circ}$ with the horizontal is placed in an open rainy field as shown,near another cylindrical container having the same base area $A$. The ratio of the rates of collection of water in the two containers will be:

$A$ table tennis ball has radius $(3 / 2) \times 10^{-2} \text{ m}$ and mass $(22 / 7) \times 10^{-3} \text{ kg}$. It is slowly pushed down into a swimming pool to a depth of $d = 0.7 \text{ m}$ below the water surface and then released from rest. It emerges from the water surface at speed $v$,without getting wet,and rises up to a height $H$. Which of the following option$(s)$ is (are) correct?
[Given: $\pi = 22 / 7, g = 10 \text{ ms}^{-2}$,density of water $= 1 \times 10^3 \text{ kg m}^{-3}$,viscosity of water $= 1 \times 10^{-3} \text{ Pa-s}$.]
$(A)$ The work done in pushing the ball to the depth $d$ is $0.077 \text{ J}$.
$(B)$ If we neglect the viscous force in water,then the speed $v = 7 \text{ m/s}$.
$(C)$ If we neglect the viscous force in water,then the height $H = 1.4 \text{ m}$.
$(D)$ The ratio of the magnitudes of the net force excluding the viscous force to the maximum viscous force in water is $500 / 9$.

Given below are two statements:
Statement-$I$: The hot water flows faster than cold water.
Statement-$II$: Soap water has higher surface tension as compared to fresh water.
In the light of the above statements,choose the correct answer from the options given below: