Question

Two rods A and B. each of equal length but different materials are suspended from a common support as shown in the figure. The roads A and B can support a maximum load of $W_1$ = 600 N and $W_2$ = 6000 N, respectively. If their cross-sectional areas are $A_1$ = $10m{m}^2$ and $A_2$ = 1000 $m{m}^2,$ respectively, then identify the stronger material.

Answer 1

At first sight. it looks that rod B is stronger as it supports a larger load. But we cannot compare strengths without having a common basis of comparison. Since the rods have different cross-sectional area, therefore, the strengths can be compared by determining the load capacity per unit area.

For rod A

${\sigma }_1=\frac{W_1}{A_1}=\frac{600N}{10m{m}^2}=\frac{600}{10\times {10}^{-6}}=60\times {10}^{6}N{m}^{-2}$

For rod B

${\sigma }_2=\frac{W_2}{A_2}=\frac{6000N}{1000m{m}^2}=\frac{6000}{1000\times {10}^{-6}}=6\times {10}^{6}N{m}^{-2}$

$\frac{6000}{1000\times {10}^{-6}}=6\times {10}^{6}N{m}^{-2}$

Since ${\sigma }_1>{\sigma }_2$,therefore the material of rod A is stronger than that of rod B.