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

  • question_answer
    Two wires A and B are of same materials. Their lengths are in the ratio 1 : 2 and diameters are in the ratio 2 : 1 when stretched by force \[{{F}_{A}}\] and \[{{F}_{B}}\] respectively they get equal increase in their lengths. Then the ratio \[{{F}_{A}}/{{F}_{B}}\] should be [Orissa JEE 2002]

    A) 1 : 2    

    B)             1 : 1

    C)             2 : 1    

    D)             8 : 1

    Correct Answer: D

    Solution :

                    \[F=Y\times A\times \frac{l}{L}\]Þ \[F\propto \frac{{{r}^{2}}}{L}\] (Y and l are constant)             \[\frac{{{F}_{A}}}{{{F}_{B}}}={{\left( \frac{{{r}_{A}}}{{{r}_{B}}} \right)}^{2}}\times \left( \frac{{{L}_{B}}}{{{L}_{A}}} \right)={{\left( \frac{2}{1} \right)}^{2}}\times \left( \frac{2}{1} \right)=\frac{8}{1}\]


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