$A$ hemispherical bowl just floats without sinking in a liquid of density $1.2 \times 10^3 \ kg/m^3$. If the outer diameter and the density of the bowl are $1 \ m$ and $2 \times 10^4 \ kg/m^3$ respectively,then the inner diameter of the bowl will be........ $m$.

$A$ cork of density $0.5 \, g/cm^3$ floats on a calm swimming pool. The fraction of the cork's volume which is under water is ........ $\%$

Four identical beakers contain the same amount of water as shown below. Beaker $A$ contains only water. $A$ lead ball is held submerged in beaker $B$ by a string from above. $A$ same-sized plastic ball,say a table tennis $(TT)$ ball,is held submerged in beaker $C$ by a string attached to a stand from outside. Beaker $D$ contains a same-sized $TT$ ball which is held submerged by a string attached to the bottom of the beaker. These beakers (without the stand) are placed on weighing pans and register readings $w_{A}, w_{B}, w_{C}$,and $w_{D}$ for $A, B, C$,and $D$,respectively. Effects of the mass and volume of the stand and string are to be neglected.

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

When does a body float on the surface of a liquid?

$A$ wooden cube just floats inside water with a $200 \,g$ mass placed on it. When the mass is removed,the cube floats with its top surface $2 \,cm$ above the water level. The side of the cube is ......... $cm$.