question_answer

A container of height 10 m which is open at the top, has water to its full height. Two small openings are made on the wall of the container .one exactly at the middle and the other at the bottom. The ratio of the velocities with which water comes out from the middle and the bottom region respectively is

A)  \[2\]

B)  \[\frac{1}{2}\]

C)  \[\sqrt{2}\]

D)  \[\frac{1}{\sqrt{2}}\]

Correct Answer: D

Solution :

Velocity of efflux \[=\sqrt{2gh}\] Here,   \[{{h}_{1}}=\frac{H}{2}\] \[\therefore \] \[{{v}_{1}}=\sqrt{2g\frac{H}{2}}\] and \[{{h}_{2}}=H\] \[\therefore \]\[{{v}_{2}}=\sqrt{2gH}\] \[\Rightarrow \] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{\sqrt{2g\frac{H}{2}}}{\sqrt{2gH}}=\frac{1}{\sqrt{2}}\]