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 \(= 10^3\, kg\, m^{-3}\))

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Answer & Solution

Correct Answer

(B) \(9.6\)

Step-by-step Solution

Detailed explanation

\({h_1}{\rho _1}g + {h_2}{\rho _2}g = \frac{1}{2}{\rho _1}{v^2}\)

\( \Rightarrow 1000 \times 10 \times 3 + 800 \times 10 \times 2\)

\( = \frac{1}{2} \times 1000 \times {v^2}\)

\( \Rightarrow {v^2} = 2 \times \frac{{46000}}{{1000}}\)

\( \Rightarrow v = \sqrt {92} = 9.6\,m/s\)

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