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 rods $A$ and $B$ can support a maximum load of $W_1=600\text{N}$ and $W_2=6000\text{N}$ respectively. If their cross-sectional areas are $A_1=10{\text{mm}}^2$ and $A_2=1000{\text{mm}}^2$, respectively, then the stronger material is:

• A. Material $A$
• B. Material $B$
• C. Both have same strength
• D. Cannot comment

Answer 1

The correct option is A Material $A$

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, the strengths can be compared by determining the load capacity per unit area i.e. stress.
For rod $A$:
${\sigma }_1=\frac{W_1}{A_1}=\frac{600\text{N}}{10{\text{mm}}^2}=\frac{600}{10\times {10}^{-6}}=60\times {10}^6{\text{Nm}}^{-2}$
For rod $B$:
${\sigma }_2=\frac{W_2}{A_2}=\frac{6000\text{N}}{1000{\text{mm}}^2}=\frac{6000}{1000\times {10}^{-6}}=6\times {10}^6{\text{Nm}}^{-2}$
Since ${\sigma }_1>{\sigma }_2$, the material of rod $A$ is stronger than that of rod $B$.