Let l be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle `theta` with AB. The moment of inertia of the plate about the axis CD is then equal to

Options

A. `(a)I_(0)`
B. `(b)I_(0)costheta`
C. `(c)I_(0)cos^(2)theta`
D. (d)None of these

Explanation

To find the moment of inertia of a uniform square plate about an axis CD that passes through its center and makes an angle θ with the axis AB, we can use the perpendicular axis theorem and properties of symmetry. Here’s the step-by-step solution:

### Step 1: Understand the Configuration
- Let the moment of inertia of the square plate about the axis AB (which is parallel to two sides of the square) be denoted as \( I_{AB} \).
- The axis CD makes an angle θ with the axis AB and also passes through the center of the plate.

**Hint**: Visualize the square plate and the axes to understand their orientations.

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