Properties Of Solids And Liquids Question 196

Question: 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) [IIT JEE 2004]

Options:

A)50 m2/s2

B)50.5 m2/s2

C)51 m2/s2

D)52 m2/s2

Show Answer

Answer:

Correct Answer: A

Solution:

Let A = cross-section of tank

a = cross-section hole

V = velocity with which level decreases

v = velocity of efflux From equation of continuity

av=AVV=avA

By using Bernoulli’s theorem for energy per unit volume

Energy per unit volume at point A = Energy per unit volume at point B

P+ρgh+12ρV2=P+0+12ρv2

therefore v2=2gh1(aA)2=2×10×(30.525)1(0.1)2=50(m/sec)2



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