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Tube filled with liquid rotated about one end: angular velocity from the force on the far end

The same question, asked 2 times: 29 Jul 2022*, 22 Jan 2025. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    29 Jul 2022

    111
    A tube of length 50 cm50\text{ }cm is filled completely with an incompressible liquid of mass 250 g250\text{ }g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity xFrad s−1x\sqrt{F}{rad\text{ }s}^{- 1}. If FF be the force exerted by the liquid at the other end then the value of xx will be ____\_\_\_\_.

  2. Question 2

    22 Jan 2025

    99
    A tube of length 1 m is filled completely with an ideal liquid of mass 2 M, and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is FαM\sqrt{\frac{F}{\alpha M}} in SI unit. The value of α\alpha is_____