A tank of cross-sectional area A0 is filled with a non-viscous liquid. A small orifice of area A (<<A0) is present at the bottom of tank. At a moment the height of liquid in the tank is H, what is the acceleration of top layer of liquid at this moment?

Velocity of efflux =2gh∴Velocity of top layer =A2ghA0∴ Acceleration of top layer =AA02g×12hdhdt=AA02g

A tank of cross-sectional area A0 is filled with a non-viscous liquid. A small orifice of area A (<<A0) is present at the bottom of tank. At a moment the height of liquid in the tank is H, what is the acceleration of top layer of liquid at this moment?

Velocity of efflux =2gh∴Velocity of top layer =A2ghA0∴ Acceleration of top layer =AA02g×12hdhdt=AA02g

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A tank of cross-sectional area A₀ is filled with a non-viscous liquid. A small orifice of area A (<<A₀) is present at the bottom of tank. At a moment the height of liquid in the tank is H, what is the acceleration of top layer of liquid at this moment?

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$\frac{A}{A_{0}} g$

${(\frac{A}{A_{0}})}^{2} g$

Depends on H

answer is C.

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Detailed Solution

Velocity of efflux $= \sqrt{2 gh}$
$∴$ Velocity of top layer $= \frac{A \sqrt{2 gh}}{A_{0}}$
$∴$ Acceleration of top layer $= \frac{A}{A_{0}} \sqrt{2 g} \times \frac{1}{2 \sqrt{h}} \frac{dh}{dt} = {(\frac{A}{A_{0}})}^{2} g$

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