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 $\omega.$ The force exerted by the liquid at the other end is
Let the length of a small element of tube be dx. Mass of this element
$\hspace15mm dm= \frac {M}{L}dx$
where Mis mass of filled liquid and Lis length of tube.
Force on this element,
$\hspace15mm dF=dm \times x \omega^2$$\hspace15mm \int _0^FdF= \frac {M}{L}\omega^2 \int _0^Lxdx$
or $\hspace15mm F= \frac {M}{L}\omega^2 \bigg [\frac {L^2}{2}\bigg ]=\frac {ML\omega^2}{2}$
or $\hspace15mm F=\frac {1}{2}ML\omega^2$
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Top Questions on System of Particles & Rotational Motion
The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.