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}} $
