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JEE Main 2019 (12 Jan, Shift 2) · Pressure in a Fluid

Pressure in a Fluid question from JEE Main 2019 (12 Jan, Shift 2)

Q24JEE Main 2019 · 12 JAN · SHIFT 2Difficult

Pressure in a Fluid

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be:

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Answer: (a)

  1. Height difference for a rotating liquid: h=ω2r22gh = \dfrac{\omega^2 r^2}{2g}.
  2. ω=2πf=4π rad/s\omega = 2\pi f = 4\pi\text{ rad/s}, r=0.05 mr = 0.05\text{ m}.
  3. h=16π2×0.00252×9.8≈0.020 m=2.0 cmh = \dfrac{16\pi^2\times0.0025}{2\times9.8} \approx 0.020\text{ m} = 2.0\text{ cm}
  4. So the answer is (a) 2.0.
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