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

  • question_answer
    Two wires of the same material have lengths in the ratio 1 : 2 and their radii are in the ratio \[1:\sqrt{2}\]. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio                                           [MP PET 1994]

    A)                 \[2:\sqrt{2}\]         

    B)                 \[\sqrt{2}:2\]

    C)                 1 : 1       

    D)                 1 : 2

    Correct Answer: C

    Solution :

        \[l=\frac{FL}{\pi {{r}^{2}}Y}\]\[\Rightarrow l\propto \frac{L}{{{r}^{2}}}\]        (F and Y are constant)             \[\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{{{L}_{1}}}{{{L}_{2}}}{{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}=\frac{1}{2}{{\left( \sqrt{2} \right)}^{2}}\]\\[\frac{{{l}_{1}}}{{{l}_{2}}}=1:1\]


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