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RAJASTHAN PMT Rajasthan - PMT Solved Paper-2006

  • 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 the scale. What would the scale read for the length of the wire when both are ac \[40{}^\circ C\]? Given: \[\alpha \] for steel \[=11\times {{10}^{-6}}{{/}^{\text{o}}}C\] and \[\alpha \] for \[Cu=17\times {{10}^{-6}}\,{{/}^{\text{o}}}C\]:

    A)  80.0096 cm                        

    B)         80.0272 cm                        

    C)         1 cm                                     

    D)         25.2 cm

    Correct Answer: A

    Solution :

    Using the relation                 \[{{l}_{1}}={{l}_{0}}(1+\alpha t)\]                 \[=1\times [1+1]\times {{10}^{-6}}\times ({{40}^{o}}-{{20}^{o}})]\]                 \[=1.00022\,\,cm\] Now, length of copper rod at\[{{40}^{o}}C\]                 \[l_{1}^{}=l_{0}^{}(1+\alpha t)\]                 \[=80\,\,[1+17\times {{10}^{-6}}({{40}^{o}}-{{20}^{o}})]\]                 \[=80.0272\,\,cm\] Now, number of cms observed on the scale.                 \[=\frac{80.0272}{1.00022}=80.0096\]


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