SATHEE: Properties Of Solids And Liquids Question 245

Properties Of Solids And Liquids Question 245

Question: A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both the hole are the same. Then R is equal to

Options:

A) $2 π L$

B) $\frac{L}{\sqrt{2 π}}$

C) $L$

D) $\frac{L}{2 π}$

Show Answer

Answer:

Correct Answer: B

Solution:

[b] Velocity of efflux when the hole is at depth h. $v = \sqrt{2 g h}$

Rate of flow of water form square hole $Q_{1} = a_{1} v_{1} = L^{2} \sqrt{2 g y}$

Rate of flow of water from circular hole $Q_{2} = a_{2} v_{2} = π R^{2} \sqrt{2 g (4 y)}$

According to problem, $Q_{1} = Q_{2}$

$\Rightarrow L^{2} \sqrt{2 g y} = π R^{2} \sqrt{2 g (4 y)} \Rightarrow R = \frac{L}{\sqrt{2 π}}$

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Properties Of Solids And Liquids Question 245

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