If the ratio of length,radii,and Young's modulus of steel and aluminium wire are $a, b, c$ respectively,then the corresponding ratio of increase in their length would be:

Two wires of diameter $0.25 \; cm,$ one made of steel and the other made of brass,are loaded as shown in the figure. The unloaded length of the steel wire is $1.5 \; m$ and that of the brass wire is $1.0 \; m.$ Compute the elongations of the steel and the brass wires. (Given: Young's modulus of steel $Y_s = 2.0 \times 10^{11} \; Pa,$ Young's modulus of brass $Y_b = 0.91 \times 10^{11} \; Pa$)

If the density of the material increases,the value of Young's modulus

For a solid rod,the Young's modulus of elasticity is $3.2 \times 10^{11} \, N m^{-2}$ and density is $8 \times 10^3 \, kg m^{-3}$. The velocity of longitudinal wave in the rod will be $......... \times 10^{3} \, m s^{-1}$.

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3A$. If the length of the first wire is increased by $\Delta l$ on applying a force $F$,how much force is needed to stretch the second wire by the same amount?

$A$ rod is fixed between two points at $20\,^oC$. The coefficient of linear expansion of the material of the rod is $1.1 \times 10^{-5}/\,^oC$ and Young's modulus is $1.2 \times 10^{11}\,N/m^2$. Find the stress developed in the rod if the temperature of the rod becomes $10\,^oC$.