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

Determine the equation for the volume of the partially immersed part of a body floating in a fluid.

$A$ small wooden ball of density $\rho$ is immersed in water of density $\sigma$ to a depth $h$ and then released. The height $H$ above the surface of water up to which the ball will jump out of water is

$A$ cube of side $40 \ cm$ is floating with $\frac{1}{4}$th of its volume immersed in water. When a circular disc is placed on the cube, it floats with $\frac{2}{5}$th of its volume immersed in water. The mass of the disc is (in $kg$)

Assertion $(A)$: $A$ helium-filled balloon does not rise indefinitely in the air but halts after a certain height.
Reason $(R)$: Viscosity opposes the motion of the balloon. Choose any one of the following four responses:

Two solids $P$ and $Q$ float in water. It is observed that $P$ floats with half of its volume immersed and $Q$ floats with $\frac{2}{3}$ of its volume immersed. The ratio of densities of $P$ and $Q$ is