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(C) The rate of flow of water through a hole is given by the product of the velocity of efflux and the area of the hole.$\frac{\Delta V}{\Delta t} = v

Vedclass · Accepted Answer

$2.5$

Vedclass · Answer

(C) The rate of flow of water through a hole is given by the product of the velocity of efflux and the area of the hole.$\frac{\Delta V}{\Delta t} = v 	imes A$Using Torricelli's law, the velocity of efflux is $v = \sqrt{2gh}$.Thus, $\frac{\Delta V}{\Delta t} = \sqrt{2gh} 	imes A$ ... $(i)$Given:$h = 20 \,m$$g = 10 \,m/s^2$$\frac{\Delta V}{\Delta t} = 3 	imes 10^{-3} \,m^3/min = \frac{3 	imes 10^{-3}}{60} \,m^3/s = 0.5 	imes 10^{-4} \,m^3/s = 5 	imes 10^{-5} \,m^3/s$Substituting the values into equation $(i)$:$5 	imes 10^{-5} = \sqrt{2 	imes 10 	imes 20} 	imes A$$5 	imes 10^{-5} = \sqrt{400} 	imes A$$5 	imes 10^{-5} = 20 	imes A$$A = \frac{5 	imes 10^{-5}}{20} = 0.25 	imes 10^{-5} \,m^2 = 2.5 	imes 10^{-6} \,m^2$Since $1 \,m^2 = 10^6 \,mm^2$, we have:$A = 2.5 	imes 10^{-6} 	imes 10^6 \,mm^2 = 2.5 \,mm^2$.

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