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Question

# A large tank 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 H/η,(η>1) and it takes T2 time to take out the rest of water. If T1=T2, then the value of η will be

A
2
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B
3
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C
4
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D
22
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Solution

## The correct option is C 4Velocity of water coming out of orifice is given by ρgh=ρv2/2⇒v=√2ghVolume flowing out per second is A×v=−d(Ah)/dt⇒√2gdt=−dh/sqrth√2g∫T10=−(2√h)|H/nHRightarrow√2gT1=2√H−2√H/nas, H/n→0√2gT1=2√H√H−√H/n=√H/n⇒n=4

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