$A$ boat containing some iron pieces is floating in a pond. If the iron pieces are thrown into the water,the level of the water will:

$A$ stream-lined body falls through air from a height $h$ on the surface of a liquid. Let $d$ and $D$ denote the densities of the materials of the body and the liquid respectively. If $D$ > $d$, then the time after which the body will be instantaneously at rest is

State and prove Archimedes' principle.

$Assertion$ : $A$ balloon filled with hydrogen will fall with acceleration $\frac{g}{6}$ on the moon.
$Reason$ : Moon has no atmosphere.

$A$ solid sphere of specific gravity $27$ has a concentric spherical cavity and it just sinks in water. The ratio of the cavity radius to the outer radius of the sphere is

$A$ uniform solid cylinder of density $0.8 \ g/cm^3$ floats in equilibrium in a combination of two non-mixing liquids $A$ and $B$ with its axis vertical. The densities of liquids $A$ and $B$ are $0.7 \ g/cm^3$ and $1.2 \ g/cm^3$,respectively. The height of liquid $A$ is $h_A = 1.2 \ cm$ and the length of the part of the cylinder immersed in liquid $B$ is $h_B = 0.8 \ cm$. Then the length of the part of the cylinder in air is ....... $cm$.