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 y, \[t=\frac{\rho L}{2K\theta }{{y}^{2}}\] Hence, time intervals to change thickness from 0 toy, from y to 2y and so on will be in the ratio \[\Delta {{t}_{1}}:\Delta {{t}_{2}}:\Delta {{t}_{3}}::({{1}^{2}}-{{0}^{2}}):({{2}^{2}}-{{1}^{2}}):({{3}^{2}}-{{2}^{2}})\] Or \[\Delta {{t}_{1}}:\Delta {{t}_{2}}:\Delta {{t}_{3}}::1:3:5\] According to question,\[\Delta {{t}_{1}}=12\text{ }min\] Hence, \[\Delta {{t}_{2}}=3\Delta {{t}_{1}}=3\times 12\,\min \] = 36 min
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