If the ratio of diameters,lengths and Young's moduli of steel and brass wires shown in the figure are $p, q$ and $r$ respectively,then the corresponding ratio of increase in their lengths would be

$A$ steel rod of radius $20 \ mm$ and length $2 \ m$ is acted upon by a force of $400 \ kN$ along its length. The values of stress and strain are respectively $(Y_{\text{steel}} = 2 \times 10^{11} \ N \ m^{-2})$.

$A$ wire of length $0.5 \ m$ and area of cross-section $4 \times 10^{-6} \ m^2$ at a temperature of $100^{\circ} C$ is suspended vertically by fixing its upper end to the ceiling. The wire is then cooled to $0^{\circ} C$,but is prevented from contracting,by attaching a mass at the lower end. If the mass of the wire is negligible,then the value of the mass attached to the wire is (Young's modulus of material of the wire $= 10^{11} \ N \ m^{-2}$; coefficient of linear expansion of the material of the wire $= 10^{-5} \ K^{-1}$ and acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $kg$)

Two wires $A$ and $B$ of same length,same radius and same Young's modulus are heated to the same range of temperatures. If the coefficient of linear expansion of $A$ is $\frac{3}{2}$ times that of $B$,then the ratio of the thermal stresses produced in the two wires $A$ and $B$ is

$A$ structural steel rod has a radius of $10\,mm$ and length of $1.0\,m.$ $A$ $100\,kN$ force stretches it along its length. Young's modulus of structural steel is $2 \times 10^{11}\,N/m^2.$ The percentage strain is about ....... $\%$

Two wires each of radius $0.2\,cm$ and negligible mass, one made of steel and the other made of brass, are loaded as shown in the figure. The elongation of the steel wire is $.........\times 10^{-6}\,m$. [Young's modulus for steel $= 2 \times 10^{11}\,N/m^2$ and $g = 10\,m/s^2$]