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NEET Sample Paper NEET Sample Test Paper-40

  • question_answer
    Two similar springs P and Q have spring constants \[{{K}_{P}}\]and \[{{K}_{Q}}\]such that\[{{K}_{P}}>{{K}_{Q}}\]. They are stretched first by the same amount (case a), then by the same force (case b). The work done by the springs \[{{W}_{P}}\]and \[{{W}_{Q}}\]are related as, in case and case [b], respectively.

    A) \[{{W}_{p}}={{W}_{Q}};{{W}_{p}}>{{W}_{Q}}\]

    B)  \[{{W}_{p}}={{W}_{Q}};{{W}_{p}}={{W}_{Q}}\]

    C) \[{{W}_{p}}={{W}_{Q}};{{W}_{Q}}>{{W}_{p}}\]

    D) \[{{W}_{p}}<{{W}_{Q}};{{W}_{Q}}<{{W}_{p}}\]

    Correct Answer: C

    Solution :

     Case [a]: Springs are stretched by the same amount The work done by the springs \[W=\frac{1}{2}K{{x}^{2}}\] Hence\[W\propto K\] As \[{{K}_{p}}>{{K}_{Q}}\]it means \[{{W}_{p}}>{{W}_{Q}}\] Case [b]: Springs are stretched by the same force. \[F={{K}_{p}}{{X}_{p}}={{K}_{Q}}{{X}_{Q}}\] The work done by the springs \[W=\frac{1}{2}K{{x}^{2}}=\frac{1}{2}K{{\left( \frac{F}{K} \right)}^{2}}=\frac{1}{2}\frac{{{F}^{2}}}{K}\] Hence \[W\propto \frac{1}{K}\]it means \[{{W}_{Q}}>{{W}_{p}}\]


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