The weight of a body in water is one-third of its weight in air. The density of the body is ....... $g/cm^3$. (in $.5$)

$A$ person is sitting in a boat floating in a lake. This person fills a bucket of water from the lake and puts it in the boat. Will the water level in the lake go down? Explain.

When does a body sink in a liquid? Explain.

$A$ 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 $\text{g/cm}^3$?

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

As shown in the figure,a container is filled with a liquid of density $2d$ up to a height of $H/2$ and a liquid of density $d$ above it up to a height of $H/2$. $A$ solid cylinder of cross-sectional area $A/5$ and length $L$ $(L < H/2)$ is placed vertically in this container. The cylinder floats vertically such that its lower end is at a distance of $L/4$ from the interface of the two liquids. Find the density $D$ of the cylinder. (The atmospheric pressure at the surface of the upper liquid is $P_0$.)