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 $r$ and the speed of revolution is $n$ rotations/second, find the difference in height of the liquid at the center of vessel and its sides.

A tube filled with water and closed at both ends uniformly rotates in a horizontal plane about the $OO\text{'}$ axis. The manometers $A$ and $B$ fixed in the tube at distances $r_1$ and $r_2$ from rotational axis indicate pressures and $p_1$ and $p_2,$ respectively. Determine the angular velocity $\omega$ of rotation of the tube.

Figure shows a crude type of atomizer. When bulb $A$ is compressed, air flows swiftly through tube $BC$ causing a reduced pressure in the particles of the vertical tube. Liquid rises in the tube, enters $BC$ and is sprayed out. If the pressure in the bulb is $P_a+P$, where $P$ is the gauge pressure and $P_a$ is the atmospheric pressure, $P_a$ is the speed of air in $BC$, find how large would $v$ need to be to cause the liquid to rise to $BC$. Density of air $=1.3\mathrm{}\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$.

A cubic block of side $a$ is connected with two similar vertical springs as shown. Initially, bottom surface of the block of density $\sigma$ touches the surface of the fluid of density $2\sigma$ while floating. A weight is placed on the block so that it is immersed half in the fluid, find the weight.

In the arrangement as shown, $m_B=3m,$ density of liquid is $\rho$ and density of block $B$ is $2\rho .$ The system is released from rest so that block $B$ moves up when in liquid and moves down when out of liquid with the same acceleration. Find the mass of blocks $A.$

A U-Shaped tube contains a liquid of density $\rho$ and is rotated about the left dotted line as shown in figure. Find the difference in the levels of the liquid column.