$A$ cubical block of density $\rho_{b} = 600 \ kg/m^3$ floats in a liquid of density $\rho_{l} = 900 \ kg/m^3$. If the height of the block is $H = 8.0 \ cm$, then the height of the submerged part is . . . . . . $cm$. (in $.3$)

$A$ body of density $\rho$ is dropped from rest at a height $h$ into a lake of density $\sigma$ $(\sigma > \rho)$. The maximum depth to which the body sinks before returning to float on the surface is (neglect air dissipative forces).

$A$ cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with a net acceleration of $g/3$,the fraction of volume immersed in the liquid will be:

$A$ container of liquid is in free fall. Without any liquid spilling out, does this container obey the principle of Archimedes?

An ice block floats in a liquid whose density is less than water. $A$ part of the block is outside the liquid. When the whole of the ice has melted,the liquid level will

$A$ dumbbell is placed in water of density $\rho$. It is observed that by attaching a mass $m$ to the rod,the dumbbell floats with the rod horizontal on the surface of water and each sphere exactly half submerged as shown in the figure. The volume of the mass $m$ is negligible. The value of length $l$ is