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  • A cylindrical vessel filled with water upto the height becomes empty in time <img alt="\mathrm{\mathr

A cylindrical vessel filled with water upto the height \mathrm{H} becomes empty in time \mathrm{\mathrm{t}_0} due to a small hole at the bottom of the vessel. If water is filled to a height \mathrm{4 \mathrm{H}} it will flow out in time

Option: 1

t_0


Option: 2

4 \mathrm{t}_0


Option: 3

8 \mathrm{t}_0


Option: 4

2 t_0


Answers (1)

best_answer

\mathrm{\begin{aligned} & \frac{-d h}{d t} A=a \sqrt{2 g h} \\\\ & \int \frac{-d h}{\sqrt{2 g h}}=\frac{a}{A} \int d t \end{aligned}}

 

\mathrm{\begin{aligned} & =\frac{-1}{\sqrt{2 g}} \int_H^0 \frac{d h}{h}=\frac{a}{A} \int d t \\\\ & =-\frac{1}{\sqrt{2 g}} \frac{1}{2}[0-\sqrt{H}]=\frac{a}{A} t \\\\ & t \propto \sqrt{H} \end{aligned}}

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Pankaj

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