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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2003

  • question_answer
    Two wires A and B are made from the same material. The ratio of lengths and diameters respectively are 1:2 and 2:1. If these are stretched by a force, then the ratio of these expansion of lengths will be

    A)  2 : 1             

    B)  1 : 4

    C)  1 : 8          

    D)  8 : 1

    Correct Answer: C

    Solution :

     \[Y=\frac{FL}{\pi {{r}^{2}}.\,l}\] \[\Rightarrow \] \[\frac{{{L}_{1}}}{r_{1}^{2}.{{l}_{1}}}=\frac{{{L}^{2}}}{r_{2}^{2}{{l}_{2}}}\] \[\Rightarrow \] \[\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{{{L}_{1}}}{{{L}_{2}}}\times \frac{r_{2}^{2}}{r_{1}^{2}}=\left( \frac{1}{2} \right)\times {{\left( \frac{1}{2} \right)}^{2}}\] \[\Rightarrow \] \[\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{1}{8}\]


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