question_answer

A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in \[m{{s}^{-1}}\]) through a small hole on the side wall of the cylinder near its bottom, is   AIEEE  Solved  Paper-2002

A) 10                              

B)           20    

C) \[25.5\]  

D)           5

Correct Answer: B

Solution :

By applying the Bernoulli's theorem just inside and outside the hole. Take reference line for gravitational potential energy at the bottom of the vessel.              Let \[{{p}_{0}}\] be the atmospheric pressure, \[\rho \] be the density of liquid and v be the velocity at which water is coming out.                 \[{{\rho }_{inside}}+\rho gh+0={{\rho }_{outside}}+\frac{\rho {{v}^{2}}}{2}\]              \[\Rightarrow \]   \[{{p}_{0}}+\rho gh={{p}_{0}}+\frac{\rho {{v}^{2}}}{2}\]    \[\Rightarrow \]               \[v=\sqrt{2gh}=\sqrt{2\times 10\times 20}=20\,m/s\]