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

$A$ spring balance $A$ reads $2 \,kg$ with a block of mass $m$ suspended from it. Another balance $B$ reads $3 \,kg$ when a beaker with a liquid is put on its pan. The two balances are now so arranged that the hanging mass $m$ is fully immersed inside the liquid in the beaker as shown in the figure. In this situation,

$A$ cube made of a material having a density of $0.9 \times 10^3 \ kg/m^3$ floats between water (density $1.0 \times 10^3 \ kg/m^3$) and a liquid of density $0.7 \times 10^3 \ kg/m^3$. What part of the cube is immersed in water?

$A$ cork of density $0.5 \, g/cm^3$ floats on a calm swimming pool. The fraction of the cork's volume which is under water is ........ $\%$

The diagram shows a jar filled with two non-mixing liquids $1$ and $2$ having densities ${\rho _1}$ and ${\rho _2}$ respectively. $A$ solid ball,made of a material of density ${\rho _3}$,is dropped into the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for ${\rho _1}$,${\rho _2}$ and ${\rho _3}$?

$A$ 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