Consider two wires of same material having their ratio of radii to be $2: 1$. If these two wires are stretched by equal force, then the ratio of stress produced in them is
KVPY 2020, Medium
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(a)
Let $r_1$ and $r_2$ be the radii of two wires, then
$\frac{r_1}{r_2}=\frac{2}{1}$
(given)
We know that,stress $=\frac{F}{A}$
As force applied is same, so
$\frac {(Stress)_1}{(Stress)_2}$=$\frac {A_2}{A_1}=\frac {\pi r_2^2}{\pi r_1^2}$
$=\left(\frac{r_2}{r_1}\right)^2=\left(\frac{1}{2}\right)^2=\frac{1}{4}$
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