A) 2mm
B) 4mm
C) 8mm
D) 16mm
Correct Answer: A
Solution :
[a] Ratio of radii \[{{r}_{1}}:{{r}_{2}}=1:2\] Ratio of area, \[{{A}_{1}}:{{A}_{2}}=\pi r_{1}^{2}:\pi r_{2}^{2}\] \[{{A}_{1}}:{{A}_{2}}=1:4\] \[Now,\text{ }Stres{{s}_{1}}:Stres{{s}_{2}}=4:1\] \[So,Strai{{n}_{1}}:Strai{{n}_{2}}=4:1\] \[\therefore \,\,\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{4}{1}\Rightarrow 4{{l}_{2}}={{l}_{1}}=8\] \[\therefore \,\,{{l}_{2}}=2mm\] Increase in length of B is 2 mm.
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