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A container of cross-sectional area A has a small hole of area a = A/3 at the bottom. Initially liquid is filled to height h from the base. As liquid flows out, which of the following is correct?

1. The level of liquid in the container falls at a rate of sqrt(g*h/4) m/s
2. The magnitude of acceleration of the top liquid surface is g/8 m/s²
3. The acceleration of the top liquid surface is g/3 m/s²
4. None of these

Correct answer: The magnitude of acceleration of the top liquid surface is g/8 m/s²

Solution

Rate of fall of liquid surface from continuity, then differentiate to get acceleration. With a = A/3, the rate equations and acceleration can be computed from the Torricelli equation.

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