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 \[(y_{2}^{2}-y_{1}^{2})\propto {{t}_{1}}\] ...(i) Again, \[(y_{3}^{2}-y_{2}^{2})\propto {{t}_{2}}\] ?(ii) Given: \[{{y}_{1}}=0\text{ }cm,\text{ }{{y}_{2}}=1\,cm\] \[{{y}_{3}}=2cm,{{t}_{1}}=7hour,{{t}_{2}}=?\] From (i) and (ii), 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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