$A$ weightless bag is filled with $5 \,kg$ of water and is weighed in water using a spring balance. The reading of the spring balance is (in $\,kg$)

$A$ solid floats such that its $(1/3)$rd part is above the water surface. Then,the density of the solid 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 $\text{g/cm}^3$?

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

$A$ body floats in a liquid contained in a beaker. The whole system,as shown,falls freely under gravity. The upthrust on the body due to the liquid is

$A$ body of density $\rho$ is dropped from rest at a height $h$ into a lake of density $\sigma$ $(\sigma > \rho)$. The maximum depth to which the body sinks before returning to float on the surface is (neglect air dissipative forces).