$A$ liquid flows through a horizontal tube. The velocities of the liquid in the two sections,which have areas of cross-section $A_1$ and $A_2$,are $v_1$ and $v_2$ respectively. The difference in the levels of the liquid in the two vertical tubes is $h$.

$A$ tank with a square base of area $1.0 \; m^{2}$ is divided by a vertical partition in the middle. The bottom of the partition has a small hinged door of area $20 \; cm^{2}$. The tank is filled with water in one compartment and an acid (of relative density $1.7$) in the other,both to a height of $4.0 \; m$. Compute the force (in $N$) necessary to keep the door closed.

During constant temperature, we feel colder on a day when the relative humidity is ....... $\%$

$A$ 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 $500 / 9$.

Vapour is injected at a uniform rate into a closed vessel which was initially evacuated. The pressure in the vessel:

Two vessels of equal cross-sectional area $A$ are filled with a liquid of density $d$. The height of the liquid in one vessel is $h_1$ and in the other vessel is $h_2$. When both vessels are connected,find the work done by gravity.