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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2012

  • 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 rod when both are at\[40{}^\circ C\]. Given: \[\alpha \]for steel\[=11\times {{10}^{-6}}per{}^\circ C\] and a for\[Cu=17\times {{10}^{-6}}per{}^\circ C\].

    A)  80.0096cm         

    B)  80.0272 cm

    C)  1cm                                      

    D)  25.2cm

    Correct Answer: A

    Solution :

                    Using the relation \[{{l}_{t}}={{l}_{0}}(1+\alpha t)\] \[=1\times [1+11\times {{10}^{-6}}\times (40{}^\circ -20{}^\circ )]\] \[=1.00022\text{ }cm\] Now, length of copper rod at\[40{}^\circ C\]                 \[{{R}_{t}}={{l}_{0}}(1+\alpha t)\] \[=80[1+17\times {{10}^{-6}}(40{}^\circ -20{}^\circ )]1\] \[=80.0272\text{ }cm\text{ }1\] Now, number of cms observed on the scale                 \[=\frac{80.0272}{1.00022}=80.0096\]


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