A) 1 mm
B) 2 mm
C) 4 mm
D) 8 mm
Correct Answer: A
Solution :
Key Idea: From Hooke's law, if strain is small then stress is proportional to strain, i.e., \[stress=Y\times strain\]where Y is proportionality constant called Young's modules. Young's modulus is given by \[Y=\frac{\text{longitudinal }\,\text{stress}}{\text{longitudinal strain}}\] \[Y=\frac{F/A}{\Delta l/L}\]where F is force, A is area. \[\Delta l\]is change in length and L is original length. First case, \[Y=\frac{F/A}{2/L}\] ?(i) Second case, \[Y=\frac{F/A}{\Delta l'/{{L}_{2}}}\] ?(ii) Equating Eqs. (i) and (ii), we get \[\frac{L}{2}=\frac{L/2}{\Delta l'}\] \[\Rightarrow \] \[\Delta l'=1\,mm\]
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