Question

The ration of radii of two wires of same material is $2:1$. If these wires are stretched by equal force, the ratio of stresses produced in them is

• A. $2:1$
• B. $1:2$
• C. $1:4$
• D. $4:1$

Answer 1

Answer: (C)

$1:4$

$1:4$

Formula,

$stress=\frac{F}{a}$

$\frac{S_1}{S_2}=\frac{\frac{F}{a_1}}{\frac{F}{a_2}}=\frac{a_2}{a_1}$

$\Rightarrow \frac{S_1}{S_2}={\left(\frac{r_2}{r_1}\right)}^2={\left(\frac{1}{2}\right)}^2$

$\therefore \frac{S_1}{S_2}=\frac{1}{4}$

Thus he ratio is $1:4$