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A large tank filled with water to a heig...

A large tank filled with water to a height `h` is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from h to `(h)/(2)` and from `(h)/(2)` to zero is

A

`sqrt2`

B

`(1)/(2)`

C

`sqrt2-1`

D

`(1)/(sqrt2-1)`

Text Solution

Verified by Experts

The correct Answer is:
C
According to the relation `t= (A)/(A_(H)) sqrt((2)/(g)H)- (A)/(A_(H)) sqrt((2H')/(g))`
`tt= (A)/(A_(H)) sqrt((2)/(g)) xx (sqrtH - sqrtH')`
`r prop (sqrtH- sqrtH')`
`(t_(1))/(t_(2))= (sqrtH- (sqrtH)/(2))/((sqrth)/(2)- sqrt0) = (1- (1)/(sqrt2))/((1)/((1)/(sqrt2))= sqrt2-1`
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