At what depth does a body remain in equilibrium in a liquid? Explain.

$A$ piece of steel has a weight $W$ in air,$W_1$ when completely immersed in water,and $W_2$ when completely immersed in an unknown liquid. The relative density (specific gravity) of the liquid 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 $\text{ ml}$)

$A$ body is suspended by a light string. The tensions in the string when the body is in air,when the body is totally immersed in water,and when the body is totally immersed in a liquid are respectively $40.2 \,N$,$28.4 \,N$,and $16.6 \,N$. The density of the liquid is

$A$ sphere of radius $R$ made of a material of relative density $\sigma$ has a concentric cavity of radius $r$. It just floats when placed in a tank full of water. The value of the ratio $R/r$ will be:

$A$ uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended,with its length vertical,from a fixed point by a massless spring such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is