Chhattisgarh PMT Chhattisgarh PMT Solved Paper-2010

  • question_answer
    44.      A thick copper rope of density \[1.5\times {{10}^{3}}kg/{{m}^{3}}\]and young's modulus \[5\times {{10}^{6}}N/{{m}^{2}},\text{ }8m\] in length is hung from the ceiling of a room. The increase in its length due to its own weight is

    A)  \[\text{9}\text{.6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-5}}}\text{m}\]                       

    B)  \[\text{19}\text{.6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-7}}}\text{m}\]

    C)  \[\text{19}\text{.2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-7}}}\text{m}\]                     

    D) \[\text{9}\text{.6}\,\text{m}\]

    Correct Answer: D

    Solution :

    The increase in length due to its own weight \[l=\frac{{{L}^{2}}dg}{2Y}\] \[=\frac{{{(8)}^{2}}\times 1.5\times {{10}^{3}}\times 9.8}{2\times 5\times {{10}^{6}}}\] \[=9.6\times {{10}^{-2}}m\] Hence, no option is matching.


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