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

A. increases
B. decreases
C. remains constant
D. increases if the rotation is clockwise and decreases if it is anticlockwise

Answer

To solve the problem of determining how the moment of inertia of water in a closed cylindrical tube changes when the tube is rotated about a perpendicular bisector, we can follow these steps:

### Step 1: Understand the System
We have a closed cylindrical tube that contains some water, but it is not filled to the top. The tube is lying in a horizontal plane and is rotated about a perpendicular bisector.

**Hint:** Visualize the setup: a horizontal tube with water inside, and identify the axis of rotation.

### Step 2: Identify the Axis of Rotation
The axis of rotation is the perpendicular bisector of the tube. This means that the tube is rotated around a line that divides it into two equal halves.

**Hint:** Remember that the moment of inertia depends on the distance of mass from the axis of rotation.

### Step 3: Understand the Effect of Rotation
When the tube is rotated, the water inside experiences a centrifugal force that pushes it outward from the axis of rotation. This causes the water to move away from the center of the tube.

**Hint:** Think about how centrifugal force acts on the water and how it affects the distribution of mass.

### Step 4: Analyze the Moment of Inertia
The moment of inertia (I) of a mass distribution is calculated using the formula:
\[ I = \sum m_i r_i^2 \]
where \( m_i \) is the mass of each particle and \( r_i \) is the distance from the axis of rotation. As the water is pushed outward, the distance \( r \) increases.

**Hint:** Recall that as \( r \) increases, the contribution of each mass element to the moment of inertia increases.

### Step 5: Conclusion
Since the distance of the water from the axis of rotation increases due to the centrifugal effect, the moment of inertia of the water about the axis also increases.

**Final Answer:** The moment of inertia of the water about the axis increases.