The temperature of an air bubble while rising from the bottom to the surface of a lake remains constant, but its diameter is doubled. If the pressure on the surface is $h$ meters of mercury column and the relative density of mercury is $\rho$, then the depth of the lake is: (in $\rho h$)

$A$ small air bubble is at the inner surface of the bottom of a beaker filled with cold water. Now,the water in the beaker is heated. The size of the bubble increases. The reason for this may be:

$A$ 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.

Explain why:
$(a)$ To keep a piece of paper horizontal,you should blow over,not under,it.
$(b)$ When we try to close a water tap with our fingers,fast jets of water gush through the openings between our fingers.
$(c)$ The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection.
$(d)$ $A$ fluid flowing out of a small hole in a vessel results in a backward thrust on 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.

Which of the following is not an illustration of viscosity?