question_answer

Water is filled in a cylindrical container to a height of 3 m. 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 \[(g=10\,m/{{s}^{2}})\]

A)  \[{{\left[ \frac{2G}{r}{{m}_{1}}{{m}_{2}} \right]}^{1/2}}\]            

B)        \[(\Delta l)\]     

C)        \[50{{m}^{2}}/{{s}^{2}}\]            

D)       \[50.5{{m}^{2}}/{{s}^{2}}\]

Correct Answer: A

Solution :

Let A = cross-sectional of tank a = cross-section hole V = velocity with which level decreases v = velocity of efflux From equation of continuity, av = AV \[3{{R}^{2}}=\frac{5}{{{\omega }^{2}}{{C}^{2}}}\]                    \[\Rightarrow \] By using Bemoullis theorem for energy per unit volume. Energy per unit volume at point A = energy per unit volume at point B \[\frac{\frac{1}{\omega C}}{R}=\sqrt{\frac{3}{5}}\] \[\Rightarrow \] \[\frac{{{X}_{C}}}{R}=\sqrt{\frac{3}{5}}\] \[\lambda ={{\lambda }_{1}}+{{\lambda }_{2}}\]