A) less than 7 hours
B) 7 hours
C) more than 14 hours
D) more than 7 hours but less than 14 hours
Correct Answer: C
Solution :
We know that the time of formation of ice in a lake from thickness \[{{y}_{1}}\] to \[{{y}_{2}}\] is directly proportional to \[({{y}_{2}}^{2}-{{y}_{1}}^{2})\propto {{t}_{1}}\] ?(1) Again, \[({{y}_{3}}^{2}-{{y}_{2}}^{2})\propto {{t}_{2}}\] ?(2) Given : \[{{y}_{1}}=0\,cm,\,{{y}_{2}}=1cm\] \[{{y}_{3}}=2\,cm,\,{{t}_{2}}=7\,hour,\,{{t}_{2}}=?\] From (1) and (2), we get \[\frac{y_{3}^{2}-y_{2}^{2}}{y_{2}^{2}-y_{1}^{2}}=\frac{{{t}_{2}}}{{{t}_{1}}}\] or \[\frac{{{2}^{2}}-{{1}^{2}}}{{{1}^{2}}-{{0}^{2}}}=\frac{{{t}_{2}}}{7}\] or \[\frac{3}{1}=\frac{{{t}_{2}}}{7}\] Hence, \[{{t}_{2}}=7\times 3=21\] hour
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