A) 1 : 4
B) 1 : 2
C) 2 : 1
D) 4 : 1
Correct Answer: D
Solution :
(i) Young's modulus, \[=\frac{\text{Stress}}{\text{Strain}}\] or stress =Y. strain or strain = Stress / Y or\[\Delta l=\frac{Fl}{YA};\frac{\Delta {{l}_{1}}}{\Delta {{l}_{2}}}=\frac{{{F}_{1}}{{l}_{1}}}{{{A}_{1}}{{Y}_{1}}}.\frac{{{A}_{2}}{{Y}_{2}}}{{{F}_{1}}{{l}_{1}}}\] \[{{l}_{1}}={{l}_{2}}\And {{Y}_{1}}={{Y}_{2}},{{F}_{1}}={{F}_{2}}\]\[\Rightarrow \frac{\Delta {{l}_{1}}}{\Delta {{l}_{2}}}=\frac{\pi r_{2}^{2}}{\pi r_{1}^{2}}=\frac{4{{r}^{2}}}{{{r}^{2}}}=4\]You need to login to perform this action.
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