The dimensional formula for Young's modulus is

The ratio of the areas of cross-sections of three wires is $1:2:3$ and the ratio of the Young's moduli of their materials is $3:2:1$. If the three wires are of the same length and the same stretching force is applied to the three wires, then the ratio of the elongations of the three wires is

The area of cross-section of the rope used to lift a load by a crane is $2.5 \times 10^{-4} \, m^2$. The maximum lifting capacity of the crane is $10$ metric tons. To increase the lifting capacity of the crane to $25$ metric tons,the required area of cross-section of the rope should be $......... \times 10^{-4} \, m^2$ (take $g = 10 \, m/s^2$).

What is the effect of change in temperature on the Young's modulus?

Two wires of the same material have lengths in the ratio $1 : 2$ and their radii are in the ratio $1 : \sqrt{2}$. If they are stretched by applying equal forces,the increase in their lengths will be in the ratio:

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 $Y_b = 0.91 \times 10^{11} \; Pa$)