$A$ wooden cylinder floats vertically in water with half of its length immersed. The density of wood is

$A$ uniform solid cylinder of density $0.8 \ g/cm^3$ floats in equilibrium in a combination of two non-mixing liquids $A$ and $B$ with its axis vertical. The densities of liquids $A$ and $B$ are $0.7 \ g/cm^3$ and $1.2 \ g/cm^3$,respectively. The height of liquid $A$ is $h_A = 1.2 \ cm$ and the length of the part of the cylinder immersed in liquid $B$ is $h_B = 0.8 \ cm$. Then the length of the part of the cylinder in air is ....... $cm$.

$A$ 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

$A$ wooden block floating in a bucket of water has $\frac{4}{5}$ of its volume submerged. When a certain amount of oil is poured into the bucket,it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is

$A$ rectangular block of mass $M$ and cross-sectional area $A$ floats on a liquid of density $\rho$. It is given a small vertical displacement from equilibrium; it starts oscillating with frequency $n$. Then:

$A$ man is carrying a block of a certain substance (of density $1000 \,kg/m^3$) weighing $1 \,kg$ in his left hand and a bucket filled with water and weighing $10 \,kg$ in his right hand. He drops the block into the bucket. How much load does he carry in his right hand now (in $,kg$)?