The density of a rod AB increases linearly from A to B its midpoint is O and its centre of mass is at C. four axes pass through A, B, O and C, all perpendicular to the length of the rod. The moment of inertial of the rod about these axes are `I_(A), I_(B), I_(O)` and `I_(C)` respectively.

Options

A. `I_(A)gtI_(B)`
B. `I_(C)ltI_(B)`
C. `I_(O)gtI_(C)`
D. All of these

Explanation

To solve the problem regarding the moment of inertia of a rod with linearly increasing density, we will analyze the moments of inertia about the axes passing through points A, B, O, and C.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a rod AB with a linear density that increases from point A to point B.
- The midpoint of the rod is O, and the center of mass is at point C.
- We need to find the relationship between the moments of inertia \(I_A\), \(I_B\), \(I_O\), and \(I_C\).
...