question_answer

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]

A)  50 m2/s2                                             

B)  50.5 m2/s2                                         

C)  51 m2/s2                                             

D)  52 m2/s2

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 \[P+\rho gh+\frac{1}{2}\rho {{V}^{2}}=P+0+\frac{1}{2}\rho {{v}^{2}}\] Þ \[{{v}^{2}}=\frac{2gh}{1-{{\left( \frac{a}{A} \right)}^{2}}}=\frac{2\times 10\times (3-0.525)}{1-{{(0.1)}^{2}}}=50{{(m/\sec )}^{2}}\]