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Q.

A cylindrical container of cross sectional area A is filled with water. There is a small orifice at the bottom of the container and cross sectional area of the orifice is ‘a’ = nA (n < 1). When depth of water in the container is 0.8 m, the velocity of water emerging from the orifice is (Take g=10 m/s2 )

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answer is 3.

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Detailed Solution

By equation of continuity, Q=Au=av⇒u=aAv∴ ⇒u=nvApplying Bernoulli's equation between A and B, pa+12ρu2+ρgh=pa+12ρv2⇒v2−u2=2gh⇒v2(1−n2)=2gh⇒v=2gh(1−n2)∴v=2×10×0.81−n2=41−n2m/s
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