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\pi L $
B) $ \frac{L}{\sqrt{2\pi }} $
C) L
D) $ \frac{L}{2\pi } $
Show Answer
Answer:
Correct Answer: B
Solution:
Velocity of efflux when the hole is at depth h, $ v=\sqrt{2gh} $
Rate of flow of water from square hole $ Q _{1}=a _{1}v _{1} $ = $ L^{2}\sqrt{2gy} $
Rate of flow of water from circular hole $ Q _{2}=a _{2}v _{2} $ = $ \pi R^{2}\sqrt{2g(4y)} $
According to problem $ Q _{1}=Q _{2} $
therefore$ L^{2}\sqrt{2gy}=\pi R^{2}\sqrt{2g(4y)} $
$ \Rightarrow $ $ R=\frac{L}{\sqrt{2\pi }} $
