NEET Sample Paper NEET Sample Test Paper-16

  • question_answer A liquid cools from \[50{}^\circ C\] to \[45{}^\circ C\] in 5 minutes and from \[45{}^\circ C\] to \[41.5{}^\circ C\] in the next 5 minutes. The temperature of the surrounding is

    A) \[27{}^\circ C\]

    B) \[40.3{}^\circ C\]

    C)      \[23.3{}^\circ C\]

    D)      \[33.3{}^\circ C\]

    Correct Answer: D

    Solution :

    According to Newton's law of cooling \[ms\left( \frac{{{\theta }_{1}}-{{\theta }_{2}}}{t} \right)\propto \left[ \frac{{{\theta }_{1}}+{{\theta }_{2}}}{t}-{{\theta }_{o}} \right]\] where \[{{\theta }_{2}}=\] temperature of surrounding In first case,\[ms\left( \frac{50-45}{50} \right)\propto \left[ \frac{50+45}{2}-{{\theta }_{o}} \right]\](1) In second case, \[ms\left( \frac{45-41.5}{5} \right)\propto \left[ \frac{45+41.5}{2}-{{\theta }_{0}} \right]\]           (2) Solving (1) and (2), we get\[{{\theta }_{o}}=33.3{{\,}^{o}}C\] Hence, the correction option is (d).

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