Questions

A wire is stretched by 0.01m by a certain force 'F' another wire of same material whose diameter and lengths are double to original wire is stretched by the same force then its elongation will be ....

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a

0.005m

b

0.01m

c

0.02m

d

0.04m

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detailed solution

Correct option is A

e_{1} = 0.01m = 10^{-2} m F_{1} = F_{2} = F

Let ${\mathrm{r}}_{1}=\frac{\mathrm{D}}{2},{\mathrm{r}}_{2}=\frac{2\mathrm{D}}{2}=\mathrm{D}$

l_{1} = l l_{2} = l e_{2} = ?

$\mathrm{e}\propto \frac{I}{{\mathrm{r}}^{2}}$

$\Rightarrow {\mathrm{e}}_{2}=\frac{{l}_{2}}{{l}_{1}}\mathrm{x}\frac{{{\mathrm{r}}_{1}}^{2}}{{{\mathrm{r}}_{2}}^{2}}\mathrm{x}{\mathrm{e}}_{1}=0.005\mathrm{m}$

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