A) \[{{h}_{1}}-{{h}_{2}}\]
B) \[{{h}_{1}}+{{h}_{2}}\]
C) \[\sqrt{{{h}_{1}}}-\sqrt{{{h}_{2}}}\]
D) \[\sqrt{{{h}_{1}}}+\sqrt{{{h}_{2}}}\]
Correct Answer: C
Solution :
[c] \[Let-\frac{dh}{dt}\]represent the rate of descent of water level, let A and a represent the cross-sectional areas of the container and hole respectively Then, \[-A\frac{dh}{dt}=a\sqrt{2gh}\] Or \[dt=-k\frac{dh}{\sqrt{n}}dt\] Or \[\int_{0}^{t}{dt=-k\int_{{{h}_{1}}}^{{{h}_{2}}}{\frac{1}{\sqrt{h}}dh}}\] Or \[t=-k{{\left| \frac{{{h}^{-\frac{1}{2}+1}}}{-\frac{1}{2}+1} \right|}_{{{h}_{1}}}}^{{{h}_{2}}}\] Or \[t=-2k[\sqrt{{{h}_{2}}}-\sqrt{{{h}_{1}}}]\] Or \[t\propto (\sqrt{{{h}_{1}}}-\sqrt{{{h}_{2}}})\]
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