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A cylindrical tank of height 1 \mathrm{~m} and cross section area A=4000 \mathrm{~cm}^2 is initially empty when it is kept under a tap of cross sectional area \mathrm{1 \mathrm{~cm}^2}. Water starts flowing from the tap at \mathrm{ t=0}, with a speed \mathrm{ =2 \mathrm{~m} / \mathrm{s}. } There is a small hole in the base of the tank of crosssectional area 0.5 \mathrm{~cm}^2. The variation of height of water in tank (in meters) with time \mathrm{t} is best depicted by

Option: 1


Option: 2


Option: 3


Option: 4


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\mathrm{\begin{aligned} & \frac{d m}{d t}=\rho A \frac{d h}{d t}=\rho a_0 v-\rho a_1 \sqrt{2 g h} \\\\ & \Rightarrow 4000 \frac{d h}{d t}=1 \times 2-0.5 \sqrt{2 g h} \\\\ & \text { for } t=\infty \frac{d h}{d t}=0 \\\\ & \Rightarrow 2=0.5 \sqrt{2 g h} \\\\ & h=0.8 \end{aligned}}

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jitender.kumar

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