Question

A and B are two wires. The radius of A is twice that of B. they are stretched by the same load. Then the stress on B is

• A. Equal to that on A
• B. Four times that on A
• C. Two times that on A
• D. Half that on A

Answer 1

The correct option is B Four times that on A

Stress = $\frac{Force}{Area}=\frac{F}{\pi r^2}\therefore Stress\propto \frac{1}{r^2}\Rightarrow \frac{{\left(Stress\right)}_B}{{\left(Stress\right)}_A}={\left(\frac{r_A}{r_B}\right)}^2={\left(2\right)}^2\Rightarrow (Stress{)}_B=4\times (Stress{)}_A$ [As F = constant]