A fully filled hemispherical tank of radius R has an orifice of small area a at its bottom. Time required to completely empty the tank, will be (assume that the top surface area of liquid is always much greater than the orifice area)
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a
5π2gR5/2a
b
92gπR5/2a
c
7215πR5/2ag
d
5πR5/27ag
answer is C.
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Detailed Solution
A1v1=A2v2⇒πx2−dhdt=a2gh⇒∫0tadt=− R0πR2−R−h2dh2gh⇒t=72 πR5/215 ag