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Q.

A cylindrical, tank is filled with water to a level of 3m. A hole is opened at a height of 52.5 cm from bottom. The ratio of the area of the hole to that of cross-sectional area of the cylinder is 0.1. Find the square of the velocity with which water is coming out. (g = 10 m/sec2)

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a

50 m2/sec2

b

40 m2/sec2

c

51.5 m2/sec2

d

50.5 m2/sec2

answer is A.

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Detailed Solution

Let velocity with which level decreases is v1 and velocity of efflux is v2 thenFrom equation of continuity Av1=av2⇒v1=aAv2From Bernoulli's theoremP+12ρv12+ρgh=P+0+12ρv22 v22=2gh1-v1v22=2gh1-aA2=2×10×(3-0.525)1-(0.1)2=50 m2/sec2
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