A rod of length `L` is made of a uniform length `L//2` of mass `M_(1)` and a uniform length `L//2` of mass `M_(2)`,
The `M.I` of rod about an axis passing through the geometrical center and `bot^(ar)` to length

Options

A. `(1)/(3)(M_(1)+M_(2))L^(2)`
B. `(1)/(12)(M_(1)+M_(2))L^(2)`
C. `(1)/(6)(M_(1)+M_(2))L^(2)`
D. `(1)/(4)(M_(1)+M_(2))L^(2)`

Explanation

To find the moment of inertia (M.I) of a rod composed of two different masses about an axis passing through its geometrical center and perpendicular to its length, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Lengths and Masses**:
- The total length of the rod is \( L \).
- The rod is divided into two equal halves, each of length \( \frac{L}{2} \).
- The mass of the first half is \( M_1 \) and the mass of the second half is \( M_2 \).
...