Question

The ratio of radii of two wires of same material is $3:1$. If these wires are stretched by equal force, the ratio of stresses produced in them is

• A. $1:3$
• B. $3:1$
• C. $9:1$
• D. $1:9$

Answer 1

The correct option is D $1:9$

We know, $\text{stress(S)}=\frac{\text{Force(F)}}{\text{Area(A)}}$
$\Rightarrow \text{Force(F)}=\text{Stress(S)}\times \text{Area(A)}$

Since force applied on the wires is equal.[$\because F_1=F_2$ ]
$\therefore S_1{A}_1=S_2{A}_2$
$\frac{S_1}{S_2}=\frac{A_2}{A_1}=\frac{\pi r_2^2}{\pi r_1^2}$

$\because$ given $\frac{r_1}{r_2}=3$
$\frac{S_1}{S_2}=\frac{r_2^2}{r_1^2}={\left(\frac{1}{3}\right)}^2=\frac{1}{9}$
$\therefore$ Ratio of stresses produced $\frac{S_1}{S_2}=\frac{1}{9}$