Consider a water tank as shown in the figure. It's cross-sectional area is $0.4\, m ^{2}$. The tank has an opening $B$ near the bottom whose cross-section area is $1\, cm ^{2}$. A load of $24\, kg$ is applied on the water at the top when the height of the water level is $40\, cm$ above the bottom, the velocity of water coming out the opening $B$ is $v\, ms ^{-1}$. The value of $v$, to the nearest integer, is ......$m/s$. [Take value of $g$ to be $10 \,ms ^{-2}$ ]
JEE MAIN 2021, Diffcult
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$m =24 \,kg$
$A =0.4\, m ^{2}$
$a =1 \,cm ^{2}$
$H =40 \,cm$
Using Bernoulli's equation
$\Rightarrow\left( P _{0}+\frac{ mg }{ A }\right)+\rho gH + \frac{1}{2} \rho V _{1}^{2}$
$=P_{0}+0+\frac{1}{2} \rho v^{2}.....(1)$
$\Rightarrow$ Neglecting $v _{1}$
$\Rightarrow v =\sqrt{2 gH +\frac{2 mg }{ A \rho}}$
$\Rightarrow v =\sqrt{8+1.2}$
$\Rightarrow v =3.033\, m / s$
$\Rightarrow v \simeq 3 \,m / s$
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