The moment of inertia is a measure of an object`s resistance to changes in its rotational motion. It depends on the object`s mass distribution and how it is distributed relative to its axis of rotation.

In this question, we are comparing a solid disc and a solid sphere with the same mass and radius. The moment of inertia of an object depends on its mass distribution, specifically on how the mass is concentrated around its axis of rotation.

For a solid disc, the majority of the mass is concentrated near the outer edge, while the mass of a solid sphere is evenly distributed throughout its volume. This means that the solid disc has a greater amount of mass located further from its axis of rotation compared to the solid sphere.

Since the solid disc has more mass located further from its axis of rotation, it will have a higher moment of inertia compared to the solid sphere. This is because it takes more force to produce the same amount of angular acceleration in an object with a higher moment of inertia.

Therefore, option 1 is correct: The disc has a higher moment of inertia about its center of mass than the sphere does.