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

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

TestHub · Accepted Answer

Taking a small element : thus the force excreted by this element is dF then.

$d F = (d m) ω^{2} x$

$d m = \frac{M}{L} d x$

integrating we get

$\int_{0}^{F} d F = \int_{0}^{L} \frac{M}{L} ω^{2} x d x$

$F = \frac{M}{L} ω^{2} {(\frac{x^{2}}{2})}_{0}^{L}$

$F = \frac{M ω^{2} L}{2}$

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