Question

The formation of ice is started in a lake with water at $0^{\circ} C$. When the atmospheric temperature is $-10^{\circ} C$. If time taken for $1 \,cm$ of ice to be formed is $7$ hours, the time taken for the thickness of ice to increase from $1 \,cm$ to $2 \,cm$ is :

• A. less than 7 hours
• B. 7 hours
• C. more than 14 hours
• D. more than 7 hours but less than 14 hours

Answer 1

Answer: (C)

more than 14 hours

Answer 2

We know that the time of formation of ice in a lake from thickness $y_{1}$ to $y_{2}$ is directly proportional to $\left(y_{2}{ }^{2}-y_{1}{ }^{2}\right) \propto t_{1} \ldots$ (i) Again, $\left(y_{3}{ }^{2}-y_{2}{ }^{2}\right) \propto t_{2} \ldots$ (ii) Given: $y_{1}=0 cm , y_{2}=1 cm$ $y_{3}=2 cm , t_{1}=7$ hour,$t_{2}=?$ From (i) and (ii), we get $\frac{y_{3}{ }^{2}-y_{2}{ }^{2}}{y_{2}{ }^{2}-y_{1}{ }^{2}}=\frac{t_{2}}{7}$ 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