SATHEE: Properties Of Solids And Liquids Question 260

Properties Of Solids And Liquids Question 260

Question: A tank has a hole at its bottom. The time needed to empty the tank from level $h_{1}$ to $h_{2}$ will be proportional to

Options:

A) $h_{1} - h_{2}$

B) $h_{1} + h_{2}$

C) $\sqrt{h_{1}} - \sqrt{h_{2}}$

D) $\sqrt{h_{1}} + \sqrt{h_{2}}$

Show Answer

Answer:

Correct Answer: C

Solution:

[c] $L e t - \frac{d h}{d t}$

represent the rate of descent of water level, let A and a represent the cross-sectional areas of the container and hole respectively

Then, $- A \frac{d h}{d t} = a \sqrt{2 g h}$ Or $d t = - k \frac{d h}{\sqrt{n}} d t$

Or $\int_{0}^{t} d t = - k \int_{h_{1}}^{h_{2}} \frac{1}{\sqrt{h}} d h$

Or $t = - k {| \frac{h^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1} |}_{h_{1}}^{h_{2}}$

Or $t = - 2 k [\sqrt{h_{2}} - \sqrt{h_{1}}]$ Or $t \propto (\sqrt{h_{1}} - \sqrt{h_{2}})$

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Properties Of Solids And Liquids Question 260

Question: A tank has a hole at its bottom. The time needed to empty the tank from level h1 to h2 will be proportional to

Options:

Answer:

Solution:

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Question: A tank has a hole at its bottom. The time needed to empty the tank from level $h_{1}$ to $h_{2}$ will be proportional to