A right circular cylinder has a mass $m$, radius $r$, and a height $h$. The cylinder is completely submerged in a fluid of density $\rho$, as shown in the diagram. What is the magnitude of the net force on the cylinder?

When two corks, one small and one big are taken into a vessel filled with water and released which cork will come fast on the surface of water ? Why ?

The free surface of oil in a tanker, at rest, is horizontal. If the tanker starts accelerating the free surface will be titled by an angle $\theta $. If the acceleration is $\mathrm{a}$ $\mathrm{ms}^{-2}$, what will be the slope of the free surface ?

A tall tank filled with water has an irregular shape as shown. The wall $C D$ makes an angle of $45^{\circ}$ with the horizontal, the wall $A B$ is normal to the base $B C$. The lengths $A B$ and $C D$ are much smaller than the height $h$ of water (figure not to scale). Let $p_1, p_2$ and $p_3$ be the pressures exerted by the water on the wall $A B$, base $B C$ and the wall $C D$ respectively. Density of water is $\rho$ and $g$ is acceleration due to gravity. Then, approximately

A sphere of relative density $\sigma$ and diameter $D$ has concentric cavity of diameter $d$. The ratio of $\frac{D}{d}$, if it just floats on water in a tank is: