A large tank is filled with water to height H. A small hole is made at the base. It takes time T₁ for the water level to fall from H to H/η (η > 1), and time T₂ to empty the remaining water. If T₁ = T₂, find η.
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Question

A large tank is filled with water to height H. A small hole is made at the base. It takes time T₁ for the water level to fall from H to H/η (η > 1), and time T₂ to empty the remaining water. If T₁ = T₂, find η.

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G1 Physics · Accepted Answer

Step 1: For a tank draining through a small orifice, the time to fall from height H₁ to H₂ is proportional to √H₁ − √H₂. Thus T₁ ∝ √H − √(H/η), while T₂ ∝ √(H/η). Step 2: T₁=T₂ gives √H = 2√(H/η), so η = 4. Correct answer: C.