A) 2.5 s
B) 10 s
C) 20 s
D) 5 s
Correct Answer: B
Solution :
From Newtons law of cooling \[\frac{{{\theta }_{1}}-{{\theta }_{2}}}{t}\propto \left( \frac{{{\theta }_{1}}+{{\theta }_{2}}}{2}-{{\theta }_{0}} \right)\]where, \[{{\theta }_{0}}=\] temperature of surroundings \[\therefore \] \[\frac{50-49}{{{t}_{1}}}\propto \left( \frac{50+49}{2}-30 \right)\] ...(i) and \[\frac{40-39}{{{t}_{2}}}\propto \left( \frac{40+39}{2}-30 \right)\] ...(ii) Dividing Eq. (ii) by Eq. (i), we get \[\frac{{{t}_{2}}}{{{t}_{1}}}=\frac{39}{19}\]\[\Rightarrow \] \[{{t}_{2}}=\frac{39}{19}\times 5=10\,s\]
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