A cylinder of radius $R=1\mathrm{}\mathrm{m}$ and height $H=3\mathrm{m}$, two thirds filled with water, is rotated about its vertical axis, as shown in figure. Determine the speed of rotation when
The point at the centre of the base is just exposed.

A U-tube shown in figure containing two liquids of specific gravities ${\rho }_1$ and ${\rho }_2$ is given an acceleration $a$ in the horizontal direction. What is the ratio ${\rho }_1 : {\rho }_2?$

A U- tube of length $L$contains liquid. It is mounted on a horizontal turn table rotating with an angular speed $\omega$ about one of its arms as shown in figure. Find the difference in heights $\left(h\right)$ between the liquid columns in two vertical arms.

A rock is found to weigh $w$ in air when suspend from a spring scale. When completely submerged in water while attached to the spring scale, it weighs $w_{\mathrm{submerge}}$ as shown in figure. Find the density of the rock ${\rho }_{\mathrm{rock}}$ in terms of the scale reading and the density of water.

A large block of ice $5\mathrm{m}$ thick has a vertical hole drilled through it and is floating in the middle of a lake. What is the minimum length of a rope required to scoop up a bucket full of water through the hole? Relative density of ice $=0.9.$