Q.

Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (g = 10 m/s2)

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a

50 m2/s2

b

50.5m2/s2

c

51 m2/s2

d

52 m2/s2

answer is A.

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Detailed Solution

Let A = cross-section of tanka = cross-section hole V = velocity with which level decreasesv = velocity of efflux From equation of continuity av=AV⇒V=avA    By using Bernoulli's theorem for energy per unit volume Energy per unit volume at point A                            = Energy per unit volume at point BP+ρgh+12ρV2=P+0+12ρv2⇒v2=2gh1−aA2=2×10×(3−0.525)1−(0.1)2=50(m/sec)2
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