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The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m³ of water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to

Asked in JEE Main 9th Jan 2nd Shift 2019 · Efflux speed and range

• (1) 9.6 m
• (2) 6.0 m
• (3) 2.9 m
• (4) 4.8 m

Step-by-step solution

Why the other options are wrong

• (1) comes from is twice the key, from writing h=(v²)/g and losing the factor 2 in v=√2gh.
• (2) comes from a filler between options 1 and 4; the checkable routes give 4.8 m (correct), 9.6 m (the factor 2 dropped) and 2.4 m (the factor 2 applied twice), and 6.0 is none of them.
• (3) comes from no consistent slip lands here; 2.9 m needs v=7.5 m s⁻¹, and (0.74)/(60) divided by 1.26×10⁻³ m² gives 9.8 m s⁻¹ on any reading. Applying the factor 2 twice, h=(v²)/(4g), gives 2.5 m instead.

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