Four identical rods each of mass `m` and length `l` are joined to form a rigid square frame. The frame lies in the xy plane, with its centre at the origin and the sides parallel to the x and y axes. Its moment of inertia about

Options

A. the x-axis is `(2)/(3)ml^(2)`
B. the z-axis is `(4)/(3)ml^(2)`
C. an axis parallel to the z-axis and passing through a corner is `(10)/(3)ml^(2)`
D. one side is `(5)/(3)ml^(2)`

Explanation

To find the moment of inertia of the square frame about various axes, we will analyze each option step by step.

### Step 1: Moment of Inertia about the X-axis (Ix)

1. **Identify the rods**: The square frame consists of four rods, each of mass \( m \) and length \( l \). The frame is symmetric, so we can analyze two pairs of rods.

2. **Calculate the moment of inertia for one rod about its center**:
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