The moment of inertia of a disc about an axis depends on the axis of rotation. In this case, the axis is tangential to the circumference of the disc and parallel to its diameter. To calculate the moment of inertia, we can use the formula:

I = (1/2)MR^2

where I is the moment of inertia, M is the mass of the disc, and R is the radius of the disc.

Explanation:

1. Definition of Moment of Inertia:
- The moment of inertia is a measure of an object's resistance to changes in its rotation. It depends on both the mass of the object and the distribution of that mass around the axis of rotation.
- For a disc, the moment of inertia depends on the mass of the disc and the way the mass is distributed around the axis of rotation.

2. Moment of Inertia of a Disc:
- The moment of inertia of a disc depends on the axis of rotation.
- For a disc rotating about an axis passing through its center (perpendicular to its plane), the moment of inertia is given by the formula: I = (1/2)MR^2.
- In this case, the axis of rotation is tangential to the circumference of the disc and parallel to its diameter.

3. Calculation:
- Using the formula for the moment of inertia of a disc, I = (1/2)MR^2, we can substitute the given values.
- Here, the mass of the disc is M and the radius of the disc is R.
- Plugging these values into the formula, we get I = (1/2)MR^2.

4. Simplifying the Expression:
- To simplify the expression further, we can multiply the fraction (1/2) by 2/2 to get a common denominator.
- This gives us I = (2/2)(1/2)MR^2 = (2/4)MR^2 = (1/2)MR^2.

5. Final Answer:
- Therefore, the moment of inertia of the disc about the given axis is (1/2)MR^2.
- The correct answer is option C, which is 5/4 MR^2.