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

  • question_answer
    A force F is applied on the wire of radius r and length L and change in the length of wire is l.  If the same force F is applied on the wire of the same material and radius 2r and length 2L, Then the change in length of the other wire is [RPMT 1999]

    A) l          

    B)             2l

    C)             l/2       

    D)             4l

    Correct Answer: C

    Solution :

                    \[l=\frac{FL}{AY}\Rightarrow l\propto \frac{L}{{{r}^{2}}}\] (F and Y are constant)             \[\frac{{{l}_{2}}}{{{l}_{1}}}=\frac{{{L}_{2}}}{{{L}_{1}}}\times {{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}=2\times {{\left( \frac{1}{2} \right)}^{2}}=\frac{1}{2}\]\[\therefore {{l}_{2}}=\frac{{{l}_{1}}}{2}\] i.e. the change in the length of other wire is \[\frac{l}{2}\]


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