$A$ liquid is kept in a cylindrical vessel. When the vessel is rotated about its axis,the liquid rises at its sides. If the radius of the vessel is $0.05\, m$ and the speed of rotation is $2$ revolutions per second,the difference in the heights of the liquid at the centre and at the sides of the vessel will be ...... $cm$. (Take $g = 10\, ms^{-2}$ and $\pi^2 = 10$)

Fill in the blanks:
$(i)$ The cohesive force between the molecules of liquid is more than the adhesive force between the molecules of the plate, then the angle of contact obtained is ...... (acute/obtuse) and the free surface has a shape of ...... (concave/convex).
$(ii)$ The cohesive force between the molecules of liquid is less than the adhesive force between the molecules of the plate, then the angle of contact obtained is ...... (acute/obtuse) and the free surface has a shape of ...... (concave/convex).
$(iii)$ $A$ large pressure is exerted on the surface of a liquid having a shape of .......... (concave/convex).

At a speed of .......... $m/s$,the velocity head of water is equal to the pressure head of $40\, cm$ of $Hg$.

$A$ cylindrical capillary tube of $0.2 \ mm$ radius is made by joining two capillaries $T_1$ and $T_2$ of different materials having water contact angles of $0^{\circ}$ and $60^{\circ}$,respectively. The capillary tube is dipped vertically in water in two different configurations,case $I$ and $II$ as shown in the figure. Which of the following option$(s)$ is(are) correct?
(Surface tension of water $= 0.075 \ N/m$,density of water $= 1000 \ kg/m^3$,take $g = 10 \ m/s^2$)
$(1)$ The correction in the height of the water column raised in the tube,due to the weight of water contained in the meniscus,will be different for both cases.
$(2)$ For case $I$,if the capillary joint is $5 \ cm$ above the water surface,the height of the water column raised in the tube will be more than $8.75 \ cm$. (Neglect the weight of the water in the meniscus)
$(3)$ For case $I$,if the joint is kept at $8 \ cm$ above the water surface,the height of the water column in the tube will be $7.5 \ cm$. (Neglect the weight of the water in the meniscus)
$(4)$ For case $II$,if the capillary joint is $5 \ cm$ above the water surface,the height of the water column raised in the tube will be $3.75 \ cm$. (Neglect the weight of the water in the meniscus)

We are able to squeeze snow and make balls out of it because of

Two cylindrical vessels of equal cross-sectional area of $2 \ m^2$ contain water up to heights of $10 \ m$ and $6 \ m$,respectively. If the vessels are connected at their bottom,then the work done by the force of gravity is (Density of water is $10^3 \ kg/m^3$ and $g = 10 \ m/s^2$):