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Question

# A large tank is filled with water to a height H. A small hole is made at the base of the tank. It takes T1 time to decrease the height of water to Hη(η>1), and it takes T2 time to take out the rest of the water. If T1=T2, then the value of η is

A
2
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B
3
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C
4
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D
5
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Solution

## The correct option is C 4We know that, time taken for the water to empty from height H1 to H2 which leaks from a container is given by - T=Aa√2g×( √H1−√H2 ) Now, time taken to decrease height from H to Hη is T1=Aa√2g×(√H−√Hη) ........(1) and, Time taken to decrease height from Hη to 0, T2=Aa√2g×(√Hη−√0) ........(2) According to question, T1=T2 ∴√H−√Hη=√Hη−0 [ from (1) and (2) ] ⇒√H=2√Hη ⇒η=4

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