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=AV\Rightarrow V=\frac{av}{A} $

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+\rho gh+\frac{1}{2}\rho V^{2}=P+0+\frac{1}{2}\rho v^{2} $

therefore $ v^{2}=\frac{2gh}{1-{{\left( \frac{a}{A} \right)}^{2}}}=\frac{2\times 10\times (3-0.525)}{1-{{(0.1)}^{2}}}=50{{(m/\sec )}^{2}} $



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