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NEET Sample Paper NEET Sample Test Paper-70

  • question_answer
    A wire of length L and radius r is rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of the same material but of length 2L and radius 2r is stretched with a force of 2F, the increase in its length will be

    A) l                                  

    B) 2 l                

    C) \[\frac{l}{2}\]                         

    D) \[\frac{l}{4}\]

    Correct Answer: A

    Solution :

    \[l=\frac{FL}{AY}=\frac{FL}{\pi {{r}^{2}}Y}\,\,\,\,\,\,\,\therefore \,\,\,\,\,\,l\propto \frac{FL}{{{r}^{2}}}\,\,\,\,\,(Y=constant)\] \[\therefore \,\,\,\frac{{{l}_{2}}}{{{l}_{1}}}=\frac{{{F}_{2}}}{{{F}_{1}}}\times \frac{{{L}_{2}}}{{{L}_{1}}}\,{{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}=2\times 2\times {{\left( \frac{1}{2} \right)}^{2}}=1\] \[\therefore \,\,\,\,\,{{l}_{2}}-{{l}_{1}},\,\,i.e.,\,\,increment\,\,in\,\,its\,\,length\,\,will\,\,be\,\,l\]


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