Final answer:
The moment of inertia depends on an object's mass and its shape, as these factors determine the distribution of mass around the axis of rotation and influence the object's rotational inertia and angular momentum.
Step-by-step explanation:
The moment of inertia of an object depends on both the mass of the object and its distribution in relation to the axis of rotation. Hence, the correct answer to the student's question is b) Mass and shape. It is important to note that the shape of an object helps you determine the location of the center of mass and the center of rotation. This in turn affects the rotational inertia and therefore the object's angular momentum. The larger the moment of inertia, the harder it is to change the rotational state of the object. This concept is crucial, as objects with different shapes but the same mass can have different moments of inertia due to the difference in mass distribution with respect to the axis of rotation.