A) \[5{}^\circ C\]
B) \[10{}^\circ C\]
C) \[15{}^\circ C~~~~\]
D) \[20{}^\circ C\]
Correct Answer: B
Solution :
[b] According to Newton's law of cooling, \[\frac{{{\theta }_{1}}-{{\theta }_{2}}}{t}=K\left[ \frac{{{\theta }_{1}}+{{\theta }_{2}}}{2}-{{\theta }_{0}} \right]\] In the first case, \[\frac{(60-50)}{10}=K\left[ \frac{60+50}{2}-{{\theta }_{0}} \right]\] \[1=K(55-\theta )\] ....(i) In the second case, \[\frac{(50-42)}{10}=K\left[ \frac{50+42}{2}-{{\theta }_{0}} \right]\] \[0.8=K(46-{{\theta }_{0}})\] ....(ii) Dividing (i) by (ii), we get \[\frac{1}{0.8}=\frac{55-\theta }{46-\theta }\] Or \[46-{{\theta }_{0}}=44-0.8{{\theta }_{0}}\Rightarrow {{\theta }_{0}}=10{}^\circ C\]
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