First slide

Moment of intertia

Question

A closed cylindrical tube containing some water (not filling the entire tube) is rotated about a perpendicular bisector, the moment of inertia of water about the axis

Moderate

A

increases
B

decreases
C

remains constant
D

increases if the rotation is clockwise and decreases if it is anticlockwise

Solution

Initially (Fig-1) water fills the lower part of the tube uniformly. In the rotating tube pseudo force acts on water and water moves away from the axis of rotation and is accumulated at both ends of the tube as shown in Fig -2. Since $\large I = \int {{r^2}dm}$ and r increases, moment of inertia of water in rotating tube increases.

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