$A$ block of material with density $3 \,g/cc$ is placed on a fluid of density $7 \,g/cc$. The fraction of volume of the piece of material outside the fluid 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? ....... $cm$

An object suspended by a wire stretches it by $10 \,mm$. When the object is immersed in a liquid,the elongation in the wire reduces by $\frac{10}{3} \,mm$. The ratio of the relative densities of the object and the liquid is ............

$A$ solid sphere of density $\rho_s$ which is $\eta$ times lighter than water (density $\rho_w$) is suspended in a water tank by a string tied to its base as shown in the figure. If the mass of the sphere is $m$,then the tension in the string is given by:

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 ${\rho _3}$?

$A$ cubical block of wood with a side length of $10 \ cm$ floats at the interface between oil and water,with its lower surface horizontal and $4 \ cm$ below the interface. The density of oil is $0.6 \ g/cm^3$. The mass of the block is ......... $gm$.