A solid sphere of radius $R$ and density $\rho$ is attached to one end of a mass-less spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3 p$. The complete arrangement is placed in a liquid of density $2 p$ 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 spring balance reads $200 \,gF$ when carrying a lump of lead in air. If the lead is now immersed with half of its volume in brine solution, what will be the new reading of the spring balance? specific gravity of lead and brine are $11.4$ and $1.1$ respectively ……….. $gF$

An ice berg of density $900 Kg/m^3$ is floating in water of density $1000 Kg/m^3$. The percentage of volume of ice-cube outside the water is …… $\%$

A machine is blowing spherical soap bubbles of different radii filled with helium gas.It is found that, if the bubbles have a radius smaller than $1\,cm$, then they sink to the floor in still air. Larger bubbles float in the air. Assume that the thickness of the soap film in all bubbles is uniform and equal. Assume that the density of soap solution is same as that of water $\left(=1000 \,kg m ^{-3}\right)$. The density of helium inside the bubbles and air are $0.18 \,kg m ^{-3}$ and $1.23 \,kg m ^{-3}$, respectively. Then, the thickness of the soap film of the bubbles is ………. $\mu m$ (Note $1 \,\mu m =10^{-6} \,m$ )

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