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

Answer: (B)

Four times that on A

Answer 2

Stress =$\frac{\text{Force}}{\text{Area}} = \frac{F}{\pi r^{2}}$

∴ Stress $\propto \frac{1}{r^{2}}$ ⇒ $\frac{(\text{Stress})_{B}}{(\text{Stress})_{A}} = \left( \frac{r_{A}}{r_{B}} \right)^{2} = (2)^{2}$ ⇒ (Stress)_B

= 4 × (stress)_A [As F = constant]