SATHEE: Properties Of Solids And Liquids Question 214

Properties Of Solids And Liquids Question 214

Question: A large tank filled with water to a height ?h? is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to $\frac{h}{2}$ and from $\frac{h}{2}$ to zero is [EAMCET (Engg.) 2003]

Options:

A) $\sqrt{2}$

B) $\frac{1}{\sqrt{2}}$

C) $\sqrt{2} - 1$

D) $\frac{1}{\sqrt{2} - 1}$

Show Answer

Answer:

Correct Answer: C

Solution:

Time taken for the level to fall from H to $H^{'}$

$t = \frac{A}{A_{0}} \sqrt{\frac{2}{g}} [\sqrt{H} - \sqrt{H^{'}}]$

According to problem- the time taken for the level to fall from h to $\frac{h}{2}$

$t_{1} = \frac{A}{A_{0}} \sqrt{\frac{2}{g}} [\sqrt{h} - \sqrt{\frac{h}{2}}]$

and similarly time taken for the level to fall from $\frac{h}{2}$ to zero $t_{2} = \frac{A}{A_{0}} \sqrt{\frac{2}{g}} [\sqrt{\frac{h}{2}} - 0]$

$∴ \frac{t_{1}}{t_{2}} = \frac{1 - \frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}} - 0} = \sqrt{2} - 1.$

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Properties Of Solids And Liquids Question 214

Question: A large tank filled with water to a height ?h? is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to h2 and from h2 to zero is [EAMCET (Engg.) 2003]

Options:

Answer:

Solution:

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Question: A large tank filled with water to a height ?h? is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to $\frac{h}{2}$ and from $\frac{h}{2}$ to zero is [EAMCET (Engg.) 2003]