The Young's modulus of steel is three times that of aluminum. Two wires of the same length and cross

Question

The Young's modulus of steel is three times that of aluminum. Two wires of the same length and cross-sectional area, one of steel and another of aluminum, are suspended from the same roof. If equal weights are attached to their lower ends, the ratio of the elongation produced in the steel wire to that in the aluminum wire is

Professor PC Thomas Classes · Answer

(a) : The elongation produced in a wire is given by $\Delta L = \frac{WL}{YA}$. Since both wires have the same length $L$, the same area of cross-section $A$, and are subjected to the same weight $W$, we have $\Delta L \propto \frac{1}{Y}$. Therefore, the ratio of elongations is $\frac{\Delta L_s}{\Delta L_{al}} = \frac{Y_{al}}{Y_s}$. We are given $Y_s = 3 Y_{al}$, so $\frac{Y_{al}}{Y_s} = \frac{1}{3}$. The ratio is $1 : 3$.