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A cylindrical tank has a small hole of area 2 cm² in its base. Water is fed into the tank from above at a steady rate of 100 cm³/s. Find the maximum height to which the water level can rise in the tank. (Take g = 10 m/s²)
- 1.25*10⁻² m
- 2.5*10⁻² m
- 5.5*10⁻² m
- 3.5*10⁻² m
Correct answer: 1.25*10⁻² m
Solution
Maximum height is reached at steady state, where the volume flow out equals the volume flow in. Outflow = a*sqrt(2*g*h). Set this equal to Q = 100 cm³/s = 1*10⁻⁴ m³/s, with a = 2 cm² = 2*10⁻⁴ m², and solve for h.
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