$A$ $400 \ g$ solid cube having an edge of length $10 \ cm$ floats in water. How much volume of the cube is outside the water (in $cm^3$)? (Given: density of water $= 1000 \ kg/m^3$)

$A$ 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

$A$ body when fully immersed in a liquid of specific gravity $1.2$ weighs $44 \text{ gwt}$. The same body when fully immersed in water weighs $50 \text{ gwt}$. The mass of the body is (in $\text{ g}$)

$A$ cylindrical block of area of cross-section $A$ and of material of density $\rho$ is placed in a liquid of density one-third of the density of the block. The block compresses a spring,and the compression in the spring is one-third of the length of the block. If the acceleration due to gravity is $g$,the spring constant of the spring is:

$A$ cylinder of mass $m$ and material density $\rho$ hanging from a string is lowered into a vessel of cross-sectional area $A$ containing a liquid of density $\sigma$ $(< \rho)$ until it is fully immersed. The increase in pressure at the bottom of the vessel is

Consider a solid sphere of radius $R$ and mass density $\rho(r) = \rho_{0} \left(1 - \frac{r^{2}}{R^{2}}\right)$ for $0 < r \leq R$. The minimum density of a liquid in which it will float is