A) \[1.0\times {{10}^{-4}}\]
B) \[1.5\times {{10}^{-4}}\]
C)
\[0.25\times {{10}^{-4}}\] D)
\[5\times {{10}^{-4}}\]
Correct Answer:
C Solution :
Stress \[\left( \frac{F}{A} \right)=5\times {{10}^{7}}N{{m}^{-2}}\] \[\Delta V=0.02%=2\times {{10}^{-4}}{{m}^{3}}\] \[\frac{\Delta r}{r}=?\] \[\gamma =\frac{stress}{strain}\Rightarrow strain\left( \frac{\Delta \ell }{{{\ell }_{0}}} \right)=\frac{\gamma }{stress}\]
(i) \[\Delta V=2\pi {{\ell }_{0}}\Delta r-\pi {{r}^{2}}\Delta \ell \]
(ii) From eqns (i) and (ii) putting the value of \[\Delta \ell ,{{\ell }_{0}}\]and \[\Delta V\]and solving we get \[\frac{\Delta r}{r}=0.25\times {{10}^{-4}}\]
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