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  4. Water is filled up to a height h in a cylindrical vessel. It takes time t to completely drain the vessel by means of a small hole at the bottom. If water is filled up to a height 4h then the time it takes to completely drain the vessel is

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Q. Water is filled up to a height $h$ in a cylindrical vessel. It takes time $t$ to completely drain the vessel by means of a small hole at the bottom. If water is filled up to a height $4h$ then the time it takes to completely drain the vessel is

NTA AbhyasNTA Abhyas 2022

Solution:

Time required to empty the tank,
$t=\frac{A}{A_{0}}\sqrt{\frac{2 H}{g}}\Rightarrow \frac{t_{2}}{t_{1}}=\sqrt{\frac{H_{2}}{H_{1}}}=\sqrt{\frac{8 h}{2 h}}=2$
$\therefore t_{2}=2t$