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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