A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω . The force exerted by the liquid at the other end is

Question

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω . The force exerted by the liquid at the other end is, M ω 2 L 2, M L ω 2, M L ω 2 4, M L 2 ω 2 2

MARKS App · Accepted Answer

Taking a small element : thus the force excreted by this element is dF then. d F = d m ω 2 x d m = M L d x integrating we get ∫ 0 F d F = ∫ 0 L M L ω 2 x d x F = M L ω 2 ( x 2 2 ) 0 L F = M ω 2 L 2

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