For the arrangement shown in the figure, Area of the cross section of the tank$A=\sqrt{5}{\mathrm{m}}^2$ and area of the orifice a = 4 cm². If the time interval in seconds after which the water jet ceases to cross the wall is Nx10³ sec. The value of N is ________. [Assume that the container remaining fixed]

$$\begin{gathered} For vertical motion, 1=\frac{1}{2}g{t}^2 \\ t=\frac{1}{\sqrt{5}}s \end{gathered}$$

$$\begin{gathered} To just cross the wall, velocity of efflux should be v= \sqrt{2gh} \\ where, h is the level of water above the oriffice. \\ In horizontal direction, \\ x=\sqrt{2gh}\left(\frac{1}{\sqrt{5}}\right)=2\sqrt{h} \\ \Rightarrow h=\frac{x^2}{4}=0.25m \end{gathered}$$

$\text{ (i.e. level goes down from }0.81\mathrm{m}\text{ to }0.25\mathrm{m}\text{ . Using equation of continuity) }$

$\begin{array}{l}-\sqrt{5}\cdot \frac{dh}{dt}=\sqrt{2gh}\left(4\times {10}^{-4}\right)\\ \text{ on solving }t=1000\mathrm{s}\end{array}$