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NEET Sample Paper NEET Sample Test Paper-24

  • question_answer
    A steel scale measures the length of a copper wire as 80.0 cm, when both are at \[20{}^\circ C\] (the calibration temperature for scale). What would be the scale read for the length of the wire when both are at \[40{}^\circ C\]? (Given \[{{\alpha }_{steel}}=11\times {{10}^{-6}}\]per \[{{\,}^{o}}C\] and \[{{\alpha }_{copper}}=17\times {{10}^{-6}}\]per\[{{\,}^{o}}C\])

    A)  80.0096 cm     

    B)  80.0272 cm

    C)  1 cm                           

    D)  25.2 cm

    Correct Answer: A

    Solution :

     With temperature rise (same \[25{}^\circ C\] for both), both steel scale and copper wire expand. Hence length of copper wire w.r.t. steel scale or apparent length of copper wire will increase after rise in temperature \[{{L}_{app}}=L{{'}_{cu}}-L{{'}_{steel}}\] \[=[{{L}_{0}}(1+{{\alpha }_{Cu}}\Delta \theta )-{{L}_{0}}(1+{{\alpha }_{s}}\Delta \theta )]\] \[\Rightarrow \]\[{{L}_{app}}={{L}_{0}}({{\alpha }_{Cu}}-{{\alpha }_{s}})\Delta \theta \] \[=80(17\times {{10}^{-6}}-11\times {{10}^{-6}})\times 20\] = 80.0096 cm


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