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Question
A closed cylindrical tube containing some water (not filling the entire tube) lies in a horizontal plane. If the tube is rotated about a perpendicular bisector, the moment of inertia of water about the axis __________ .
Options
increases
decreases
remains constant
increases if the rotation is clockwise and decreases if it is anticlockwise
Solution
increases
Moment of inertia of a mass is directly proportional to the square of the distance of mass from the axis of rotation.
Therefore, we have
\[I \propto r^2\]
As the tube is rotated, water is collected at the end of tube because of centrifugal force and distance from the rotation axis increases. Hence, moment of inertia increases.
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