JEE Main & Advanced Physics Elasticity Question Bank Youngs Modulus and Breaking Stress

  • question_answer
     The ratio of diameters of two wires of same material is n : 1. The length of wires are 4 m each. On applying the same load, the increase in length of thin wire will be

    A)                 \[{{n}^{2}}\] times

    B)                             n times

    C)                 2n times

    D)                             None of the above

    Correct Answer: A

    Solution :

        \[l\propto \frac{FL}{{{r}^{2}}Y}\]Þ \[l\propto \frac{1}{{{r}^{2}}}\]  \[\text{( }F,L\ \text{and }Y\text{ are constant)}\]             \[\frac{{{l}_{2}}}{{{l}_{1}}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}={{(n)}^{2}}\Rightarrow {{l}_{2}}={{n}^{2}}{{l}_{1}}\]


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