$A$ 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 ........ $\%$

$A$ hollow sphere of external radius $R$ and thickness $t$ $(t \ll R)$ is made of a metal of density $\rho$. The sphere will float in water if:

An iceberg floats in sea water with a part of it submerged. The percentage fraction of the iceberg which is unsubmerged is (Density of ice $= 0.9 \text{ g/cm}^3$, density of sea water $= 1.1 \text{ g/cm}^3$). (in $\%$)

$A$ solid cube is floating in a liquid. The coefficient of linear expansion of the cube is $\alpha$ and the coefficient of volume expansion of the liquid is $\gamma$. On increasing the temperature of the (liquid + cube) system,the cube will sink if

$A$ ball rises to the surface at a constant velocity in a liquid whose density is $3$ times greater than that of the material of the ball. The ratio of the force of friction acting on the rising ball to its weight is (in $: 1$)

$A$ boat carrying a number of large stones is floating in a water tank. What would happen to the water level if a few stones are unloaded into the water?