એક તાર (યંગ મોડ્યુલસ 2 times 10^{11}, Nm^{-2} | vedclass

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Question

$Given,\,y = 2 	imes {10^{11}}N{m^{ - 2}}$

$Stress\left( {\frac{F}{A}} ight) = 5 	imes {10^7}N{m^{ - 2}}$

$\Delta V = 0.02\%  = 2 	ime

Vedclass · Accepted Answer

$0.25	imes 10^{-4}$

Vedclass · Answer

$Given,\,y = 2 	imes {10^{11}}N{m^{ - 2}}$

$Stress\left( {\frac{F}{A}} ight) = 5 	imes {10^7}N{m^{ - 2}}$

$\Delta V = 0.02\%  = 2 	imes {10^{ - 4}}{m^3}$

$\frac{{\Delta r}}{r} = ?$

$\gamma  = \frac{{stress}}{{strain}} \Rightarrow strain\left( {\frac{{\Delta \ell }}{{{\ell _0}}}} ight) = \frac{\gamma }{{stress}}\,\,...\left( i ight)$

$\Delta V = 2\pi {\ell _0}\Delta r - \pi {r^2}\Delta \ell $                       $...\left( {ii} ight)$

From eqns $(i)$ and $(ii)$ putting the value of 

$\Delta \ell ,{\ell _0}\,and\,\Delta V\,and\,solving\,we\,get$

$\frac{{\Delta r}}{r} = 0.25 	imes {10^{ - 4}}$

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