Question

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

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

Answer 1

The correct option is D 1 : 4

$Here,r_1:r_2=2:1F_1=F_2=F\mathrm{Stress}\left(s\right)=\frac{\mathrm{force}}{\mathrm{area}}=\frac{F}{{\mathrm{\pi r}}^2}\mathrm{Therefore},s\propto \frac{1}{r^2}\frac{S_1}{S_2}=\frac{{r_2}^2}{{r_1}^2}=\frac{1^2}{2^2}=\frac{1}{4}$