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# Two wires of same material have radius in the ratio 2 : 1 and length in the ratio 1 : 2.If equal force is applied on them then ratio of stress is

$\begin{array}{1 1}(A)\;4 : 1\\(B)\;2 : 1\\(C)\;1 : 2\\(D)\;1 : 4\end{array}$

Can you answer this question?

Stress=$\large\frac{F}{a}$
$a=\pi r^2$
$a\propto r^2$
$\large\frac{a_1}{a_2}=(\frac{r_1}{r_2})^2=(\frac{2}{1})^2$
$\Rightarrow 4$
$\large\frac{S_1}{S_2}=\frac{F/a_1}{F/a_2}=(\frac{a_2}{a_1})=\frac{1}{4}$
Ratio of stress is 1 : 4
Hence (D) is the correct answer.
answered May 7, 2014