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NEET Sample Paper NEET Sample Test Paper-8

  • question_answer
    A metal wire of length L and radius r is clamped at one end to a rigid fixed support. A force F is applied at another and so that its length increase by L. The increases in length of another metal wire of length 2L and radius 2r, when stretched by a force 2F, will be:

    A)  \[2L\]                                  

    B)  \[L\]

    C)  \[L/2\]                

    D)  \[L/4\]

    Correct Answer: B

    Solution :

    As, the Young's modulus, \[Y=\frac{FL}{\pi {{r}^{2}}l}\]             \[\therefore \]     \[l\propto \frac{FL}{{{r}^{2}}}\]                 \[\Rightarrow \]               \[\frac{{{l}_{1}}}{{{l}_{2}}}=\left( \frac{{{F}_{1}}}{{{F}_{2}}} \right)\left( \frac{{{L}_{1}}}{{{L}_{2}}} \right)\left( \frac{r_{2}^{2}}{r_{1}^{2}} \right)\]                                 \[=\left( \frac{F}{2F} \right)\times \left( \frac{L}{2L} \right)\times \left( \frac{4{{r}^{2}}}{{{r}^{2}}} \right)=1:1\]                 or            \[{{l}_{1}}={{l}_{2}}=L\]


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