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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 4
We know that, time taken for the water to empty from height H1 to H2 which leaks from a container is given by -
T=Aa2g×( H1H2 )


Now, time taken to decrease height from H to Hη is
T1=Aa2g×(HHη) ........(1)
and,
Time taken to decrease height from Hη to 0,
T2=Aa2g×(Hη0) ........(2)
According to question,
T1=T2
HHη=Hη0
[ from (1) and (2) ]
H=2Hη
η=4

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