A body of density $\rho'$  is dropped from rest at a height $h$ into a lake of density $\rho$ , where $\rho > \rho '$ . Neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface.

A body remain in equilibrium at which depth of liquid ? Explain ?

Two non-mixing liquids of densities $\rho $ and $n \rho \,(n > 1)$ are put in a container. The height of each liquid is $h.$ A solid cylinder of length $L$ and density $d$ is put in this container. The cylinder floats with its axis vertical and length $\rho L (\rho < 1)$ in the denser liquid. The density $d$ is equal to

A metallic block of density $5\,gm \,cm^{-3}$ and having dimensions $5 cm × 5 cm × 5 cm$ is weighed in water. Its apparent weight will be

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 cone of radius $R$ and height $H$, is hanging inside a liquid of density $\rho$ by means of a string as shown in the figure. The force, due to the liquid acting on the slant surface of the cone is