A) \[{{27}^{o}}C\]
B) \[{{40.3}^{o}}C\]
C) \[{{23.3}^{o}}C\]
D) \[{{33.3}^{o}}C\]
Correct Answer: D
Solution :
According to Newtons law of cooling \[\frac{{{\theta }_{1}}-{{\theta }_{2}}}{t}=\left( \frac{{{\theta }_{1}}+{{\theta }_{2}}}{2}-{{\theta }_{0}} \right)\] where \[{{\theta }_{0}}\] is the temperature of the surrounding. First case ; \[\frac{50-45}{5}\propto \left( \frac{50+41.5}{2}-{{\theta }_{0}} \right)\] ?. (i) Second case ; \[\frac{(50-41.5)}{5}\propto \left( \frac{45+41.5}{2}-{{\theta }_{0}} \right)\] ?. (ii) Dividing Eq.(i) by Eq. (ii), we get \[\frac{(50-45)}{5}\times \frac{5}{(45-41.5)}=\frac{\left( \frac{50+45}{2}-{{\theta }_{0}} \right)}{\left( \frac{45+41.5}{2}-{{\theta }_{0}} \right)}\] or \[216.25-5\,{{\theta }_{0}}=166.25-3.5{{\theta }_{0}}\] or \[1.5\,{{\theta }_{0}}=50\] or \[{{\theta }_{0}}=\frac{50}{1.5}={{33.3}^{o}}C\]
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