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A vessel of cross-sectional area A contains a liquid to a height H1. If a hole having cross-sectional area a is made at the bottom of the vessel, then the time taken by the liquid level to decrease from H1 and H2 is

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a

Aag2H1−H2

b

Aa2gH1−H2

c

aAg2H1−H2

d

aA2gH1−H2

answer is B.

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Detailed Solution

Let h be the height of the water level at any instant. Then the rate of decrease of water level is −dhdt.Therefore −Adhdt=av=a2gh⇒−dhdt=aA2gh⇒−∫H1H2 dhh1/2=aA2g∫01 dt⇒−2h1/2H1H2=aA2gt⇒2H1−H2=aA2gt⇒t=Aa2gH1−H2

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