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 :
Given, \[y=2\times {{10}^{11}}\,N{{m}^{-2}}\] 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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