A) 12 min
B) less than 12 min
C) more than 12 min but less than 24 min
D) more than 24 min
Correct Answer: D
Solution :
Time taken by ice to grow a thickness of \[t=\frac{eL}{2K\theta }{{y}^{2}}\] Hence time interval to change thickness from \[0\]to\[y\], from\[y\]to\[2y\]and so on will be in the ratio \[\Delta {{t}_{1}}:\Delta {{t}_{2}}:\Delta {{t}_{3}}\] \[\therefore \] \[=(1-{{0}^{2}}):({{2}^{2}}-{{1}^{2}}):({{3}^{2}}-{{2}^{2}})\] \[\Delta {{t}_{1}}:\Delta {{t}_{2}}:\Delta {{t}_{3}}=1:3:5\] According to question\[=\Delta {{t}_{1}}<\]term is \[\Delta {{t}_{2}}=3\Delta H\] \[=3\times 12=36\,\,\min \]
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