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JIPMER Jipmer Medical Solved Paper-2003

  • question_answer
    Two bars A and B of circular cross-section and same volume made of same material are subjected under same tension. If the diameter of A is half that of B. The ratio of extension of A to B will be:

    A)  16                                         

    B)  2                            

    C)  1/4                       

    D)         4

    Correct Answer: A

    Solution :

    \[\Delta l=\frac{FL}{\pi {{r}^{2}}Y},\] But \[V=\pi {{r}^{2}}L\]  so \[L=\frac{V}{\pi {{r}^{2}}}\] \[=\frac{FV}{{{(\pi {{r}^{2}})}^{2}}Y}\propto \frac{1}{{{r}^{4}}}\] \[\frac{\Delta {{l}_{A}}}{\Delta {{l}_{B}}}={{\left( \frac{{{r}_{B}}}{{{r}_{A}}} \right)}^{4}}={{\left( \frac{{{r}_{B}}}{\frac{{{r}_{B}}}{2}} \right)}^{4}}=16\]


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