A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity $0.8$). The height of water is $3\,m$ and that of kerosene $2\,m$. When the hole is opened the velocity of fluid coming out from it is nearly ........ $ms^{-1}$ .(take $g\, = 10\, m s^{-2}$ and density of water $= 10^3\, kg\, m^{-3}$)
JEE MAIN 2014, Medium
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${h_1}{\rho _1}g + {h_2}{\rho _2}g = \frac{1}{2}{\rho _1}{v^2}$
$ \Rightarrow 1000 \times 10 \times 3 + 800 \times 10 \times 2$
$ = \frac{1}{2} \times 1000 \times {v^2}$
$ \Rightarrow {v^2} = 2 \times \frac{{46000}}{{1000}}$
$ \Rightarrow v = \sqrt {92} = 9.6\,m/s$
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