KVPY Sample Paper KVPY Stream-SX Model Paper-13

  • question_answer
    A uniform metal rod (fixed at both ends) of \[2\text{ }m{{m}^{2}}\]cross-section is cooled from \[40{}^\circ C\] to \[20{}^\circ C.\] The co-efficient of the linear expansion of the rod is \[12\times {{10}^{-\,4}}\] per degree & It's young modulus of elasticity is \[{{10}^{11}}\text{ }N/{{m}^{2}}.\]The energy stored per unit volume of the rod is -

    A) \[2880\text{ }J/{{m}^{3}}~\]

    B) \[1500\text{ }J/{{m}^{3}}\]

    C) \[5760\text{ }J/{{m}^{3}}\]     

    D) \[1440\text{ }J/{{m}^{3}}\]

    Correct Answer: A

    Solution :

    Energy Density \[=\frac{1}{2}stress\times strain\]\[=\frac{1}{2}Y{{(strain)}^{2}}=2880\,\,J/{{m}^{3}}\]

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