$A$ ball of relative density $0.8$ falls into water from a height of $2 \ m$. The depth to which the ball will sink is ........ $m$ (neglect viscous forces):

$A$ solid sphere of radius $R$ and density $\rho$ is attached to one end of a massless spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3\rho$. The complete arrangement is placed in a liquid of density $2\rho$ and is allowed to reach equilibrium. The correct statement$(s)$ is (are):
$(A)$ The net elongation of the spring is $\frac{4 \pi R^3 \rho g}{3 k}$
$(B)$ The net elongation of the spring is $\frac{8 \pi R^3 \rho g}{3 k}$
$(C)$ The light sphere is partially submerged.
$(D)$ The light sphere is completely submerged.

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

Spheres of iron and lead having the same mass are completely immersed in water. The density of lead is greater than that of iron. If the apparent loss of weight is $w_{1}$ for the iron sphere and $w_{2}$ for the lead sphere,then the ratio $\frac{w_{1}}{w_{2}}$ is:

$A$ wooden block is floating on water kept in a beaker. $40 \%$ of the block is above the water surface. Now the beaker is kept inside a lift that starts going upward with acceleration equal to $g / 2$. The block will then

An iceberg floats in water with part of it submerged. What is the fraction of the volume of the iceberg submerged if the density of ice is ${\rho _i} = 0.917 \, g/cm^3$?