SATHEE: Properties Of Solids And Liquids Question 197

Properties Of Solids And Liquids Question 197

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 holes are the same. Then R is equal to [IIT-JEE (Screening) 2000]

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:

Velocity of efflux when the hole is at depth h, $v = \sqrt{2 g h}$

Rate of flow of water from 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 $Q_{1} = Q_{2}$

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

$\Rightarrow$ $R = \frac{L}{\sqrt{2 π}}$

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Properties Of Solids And Liquids Question 197

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