A) 7
B) 6
C) 5
D) 4
Correct Answer: D
Solution :
From Newtons law of cooling Rate of cooling oc temperature difference \[\therefore \] \[\frac{{{\theta }_{1}}-{{\theta }_{2}}}{t}=K\left( \frac{{{\theta }_{1}}+{{\theta }_{2}}}{2}-{{\theta }_{0}} \right)\] Given, \[{{\theta }_{1}}={{75}^{o}}C,\,\,\,{{\theta }_{2}}{{65}^{o}}C,\,\,\,t=2\] min \[\frac{75-65}{2}=K\left( \frac{75+65}{2}-30 \right)\] \[\Rightarrow \] \[5=K\times 40\] \[\Rightarrow \] \[K=\frac{1}{8}\] When body cools from \[{{55}^{o}}C\] to \[{{65}^{o}}C\], we have \[\frac{55-45}{{{t}_{2}}}=K\left( \frac{55+45}{2}-30 \right)\] \[\Rightarrow \] \[\frac{10}{{{t}_{2}}}=\frac{1}{8}\times 20\] \[\Rightarrow \] \[{{t}_{2}}=4\,\min \]
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