In the figure shown, the heavy cylinder (radius $R$ ) resting on a smooth surface separates two liquids of densities $2\rho$ and $3p.$ Find the height $\text{'}h\text{'}$ for the equilibrium of cylinder.

A rectangular box is completely filled with a liquid of density $\rho ,$ as shown in figure. The box is accelerated horizontally with a constant acceleration $a.$ Determine the gauge pressures at the four points $A, B, C$ and $D.$

Figure shows an $L$-shaped tube filled with a liquid to a height $H.$ What should be the horizontal acceleration a of the tube so that the pressure at the point $A$ becomes atmospheric.

A container shown in figure is accelerated horizontally with acceleration $a.$ Find the minimum value of $a$ at which liquid just starts spilling out.

A cylinder of radius $a$ and height $H$ is filled with a liquid to an unknown height $h.$ When it is rotated at an unknown constant angular velocity $\omega ,$ the base of the cylinder gets exposed when the liquid just starts spilling out, as shown in figure.
(a) Find the height $h$ of the liquid.
(b) Find the angular speed $\omega$ of the cylinder.