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JEE Main & Advanced Sample Paper JEE Main Sample Paper-39

  • question_answer
    There are two wires of the same length. The diameter of second wire is twice that of the first. On applying the same load to both the wires, the extension produced in them will be in ratio of

    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\[\Delta l=\frac{Fl}{YA};\frac{\Delta {{l}_{1}}}{\Delta {{l}_{2}}}=\frac{{{F}_{1}}{{l}_{1}}}{{{A}_{1}}{{Y}_{1}}}.\frac{{{A}_{2}}{{Y}_{2}}}{{{F}_{1}}{{l}_{1}}}\] \[{{l}_{1}}={{l}_{2}}\And {{Y}_{1}}={{Y}_{2}},{{F}_{1}}={{F}_{2}}\]\[\Rightarrow \frac{\Delta {{l}_{1}}}{\Delta {{l}_{2}}}=\frac{\pi r_{2}^{2}}{\pi r_{1}^{2}}=\frac{4{{r}^{2}}}{{{r}^{2}}}=4\]


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