Two non-mixing liquids of densities $\rho $ and $n \rho \,(n > 1)$ are put in a container. The height of each liquid is $h.$ A solid cylinder of length $L$ and density $d$ is put in this container. The cylinder floats with its axis vertical and length $\rho L (\rho < 1)$ in the denser liquid. The density $d$ is equal to

The density of ice is $0.9 \,g / cm ^3$. What percentage by volume of the block of ice floats outside the water is ..........$\%$

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 ? ....... $cm$

A rectangular block is $5 cm × 5 cm × 10cm$  in size. The block is floating in water with $ 5 cm $ side vertical. If it floats with $10 cm $ side vertical, what change will occur in the level of water?

Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is $36 g $ and its density is $9 g / cm^3$. If the mass of the other is $48 g$, its density in $g / cm^3$ is

A vessel contains oil (density =$ 0.8 \;gm/cm^3$) over mercury (density = $13.6\; gm/cm^3$). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in $ gm/cm^3$ is