The moment of inertia of a circular disc of mass `M` and radius `R` about an axis passing thrugh the center of mass is `I_(0)`. The moment of inertia of another circular disc of same mass and thickness but half the density about the same axis is

Options

A. `(I_(0))/(8)`
B. `(I_(0))/(4)`
C. `8I_(0)`
D. `2I_(0)`

Explanation

To solve the problem, we need to determine the moment of inertia of a second circular disc that has the same mass and thickness as the first disc but has half the density.

### Step-by-Step Solution:

1. **Understand the Moment of Inertia of the First Disc**:
The moment of inertia \( I_0 \) of the first circular disc (mass \( M \), radius \( R \)) about an axis through its center of mass is given by the formula:
\[
I_0 = \frac{1}{2} M R^2
...