Two solids $A$ and $B$ float in water. It is observed that $A$ floats with $\frac{1}{2}$ of its body immersed in water and $B$ floats with $\frac{1}{4}$ of its volume above the water level. The ratio of the density of $A$ to that of $B$ is

State the law of floatation and describe its cases.

$A$ solid sphere of specific gravity $27$ has a concentric spherical cavity and it just sinks in water. The ratio of the cavity radius to the outer radius of the sphere is

$A$ wooden block of outer volume $1 \text{ litre}$ and specific gravity $\frac{3}{4}$ having a cavity floats with half of its volume immersed in water. Then the volume of the cavity is (in $\text{ ml}$)

$A$ piece of granite floats at the interface of mercury and water contained in a beaker as shown in the figure. If the densities of granite, water, and mercury are $\rho, \rho_1$, and $\rho_2$ respectively, the ratio of the volume of granite in water to the volume of granite in mercury is:

An object of volume $V_0$ and density $d_0$ is placed in a liquid of density $d$. What fraction of its volume remains outside the liquid?