A hole is made at the bottom of a large vessel open at the top. If water is filled to a height h it drain out completely in time t. The time taken by the water column of height 4h to drain completely is
(a). `sqrt(2t)`
(b). `2t`
(c). `2sqrt(2t)`
(d). `4t`

Answer

A

Explanation

Here `(-A(dh)/(dt))=(av)=asqrt(2gh)impliesunderset(0)overset(h)intyh^(-1//2)d=(a)/(A)sqrt(2g)underset(0)overset(h)intdtimpliest=(A)/(a)sqrt((2h)/(g))impliestpropsqrt(h)`