The weight of a sphere in air is $50 \ g$. Its weight is $40 \ g$ in a liquid at temperature $20^{\circ} C$. When the temperature increases to $70^{\circ} C$,its weight becomes $45 \ g$. The ratio of the densities of the liquid at the two given temperatures is: (in $: 1$)

Two rods $A$ and $B$ of the same length are made of the same material. The ratio of their resistances is $1 : 2$. If the rods are immersed in water,the loss in their weight will be:

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 ${\rho _3}$?

$A$ container of large surface area is filled with a liquid of density $\rho$. $A$ cubical block of side edge $a$ and mass $M$ is floating in it with four-fifths of its volume submerged. If a coin of mass $m$ is placed gently on the top surface of the block,it is just submerged. $M$ is:

Spheres of iron and lead having the same mass are completely immersed in water. The density of lead is greater than that of iron. If the apparent loss of weight is $w_{1}$ for the iron sphere and $w_{2}$ for the lead sphere,then the ratio $\frac{w_{1}}{w_{2}}$ is:

$A$ block of wood floats in water with $\frac{4}{5}$ of its volume submerged,but it just floats in another liquid. The density of the liquid is (in $kg/m^3$):