A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity x F rad s - 1 . If F be the force exerted by the liquid at the other end then the value of x will be _____ .

Step-by-step solution

Considering an element of tube of length d x having mass d m at a distance of x from right end as shown in figure below. Now, force acting of that element is F = ∫ d m ω 2 x Integrating the above relation for whole length of tube, we have F = ∫ 0 L m L d x ω 2 x = m L ω 2 L 2 2 = m ω 2 L 2 ⇒ ω = 2 m L F = 2 0 . 25 × 0 . 5 F = 16 F = 4 F   rad   s - 1 Hence, the value of x = 4 .