Two blocks of ice when pressed together join to form one block because

$A$ large number of water drops,each of radius $r$,combine to form a single drop of radius $R$. If the surface tension is $T$ and the mechanical equivalent of heat is $J$,then the rise in temperature will be:

$A$ liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the sides. If the radius of the vessel is $0.05\,m$ and the speed of rotation is $2\,rev/s$,the difference in the height of the liquid at the center of the vessel and its sides will be .............. $cm$ $(\pi^2 = 10)$.

$A$ cylindrical container is filled with liquid. When the container is rotated about its axis,the liquid rises along its sides. If the radius of the container is $r$ and the angular velocity of the container is $\omega$ rad/s,what will be the difference in the height of the liquid at the center and at the sides?

$A$ cylindrical vessel of height $500 \ mm$ has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height $H$. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vessel becomes steady with the height of the water column being $200 \ mm$. Find the fall in height (in $mm$) of the water level due to the opening of the orifice.
[Take atmospheric pressure $= 1.0 \times 10^5 \ N/m^2$,density of water $= 1000 \ kg/m^3$ and $g = 10 \ m/s^2$. Neglect any effect of surface tension.]

$A$ glass tube of uniform cross-section is filled with water and mounted on a rotatable shaft as shown in the figure. If the tube is rotated with a constant angular velocity $\omega$,then: