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A small hole of area of cross-section 2 mm² is present near the bottom of a fully filled open tank of height 2 m. Taking g=10 m/s², the rate of flow of water through the open hole would be nearly

Asked in NEET 2019 · Efflux speed and range

• (1) 6.4×10⁻⁶ m³/s
• (2) 12.6×10⁻⁶ m³/s
• (3) 8.9×10⁻⁶ m³/s
• (4) 2.23×10⁻⁶ m³/s

Step-by-step solution

Why the other options are wrong

• (1) 6.4×10⁻⁶ m³/s is almost exactly half the answer; halving needs either half the hole or half the efflux speed, and neither follows from any single slip in v=√2gh
• (3) comes from dropping the 2 under the root and using v=√gh=4.47 m s⁻¹: 2×10⁻⁶×4.47=8.9×10⁻⁶ m³/s
• (4) 2.23×10⁻⁶ m³/s needs an efflux speed of 1.12 m s⁻¹, which corresponds to a head of only 6 cm rather than the 2 m given

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