$A$ piece of gold weighs $10 \,g$ in air and $9 \,g$ in water. What is the volume of the cavity in $cc$? (Density of gold $= 19.3 \,g \,cm^{-3}$)

If $W$ is the weight of a body of density $\rho$ in vacuum,then its apparent weight in air of density $\sigma$ is:

Two cubical blocks identical in dimensions float in water in such a way that the $1$st block floats with half part immersed in water and the $2$nd block floats with $3/4$ of its volume inside the water. The ratio of densities of the blocks is ..........

$A$ container contains mercury $(\rho = 13.6 \text{ g/cm}^3)$ and oil $(\rho = 0.8 \text{ g/cm}^3)$. $A$ sphere floats such that half of its volume is in mercury and half of its volume is in oil. What is the density of the material of the sphere in $\text{g/cm}^3$?

$A$ ball whose density is $0.4 \times 10^3 \ kg/m^3$ falls into water from a height of $9 \ cm$. To what depth does the ball sink in $cm$?

An empty balloon weighs $1\, g$. The balloon is filled with water to the neck and tied with a massless thread. The weight of the balloon along with water is $101\, g$. The balloon filled with water is weighed when fully immersed in water. Its weight in water is ...... $g$.