Final answer:
The correct moment of inertia for a solid sphere rotating about its center is ⅓mr², not 2mr². The moment of inertia reflects how mass is distributed with respect to the axis of rotation and depends on the object's shape and size.
Step-by-step explanation:
The moment of inertia for a solid sphere rotating about an axis through its center is not given by just 2mr²; this statement is incorrect. The correct moment of inertia I for a solid sphere is actually ⅓mr² (2/5 times the mass of the sphere times the radius squared). Moment of inertia is a physical quantity representing the rotational inertia of a body, which determines how much torque is needed for a desired angular acceleration about a rotational axis. In this case of a solid sphere, the moment of inertia plays a crucial role in describing its rotational motion and is derived through integration over the sphere's volume. It reflects how mass is distributed in the sphere with respect to its rotating axis. mr² is only the moment of inertia for a point mass or for bodies like a hoop, where all the mass is distributed at a distance r from the axis.
As for point d, 'All of the above,' it does not apply here as the provided formula is incorrect for a solid sphere. The moment of inertia depends on the size, shape, and mass distribution of an object, as well as the location of the axis of rotation. For example, while the moment of inertia of a hoop is MR² (where M is the mass and R is the radius), different shapes have different moments of inertia, such as the ⅓ML² for a long rod spun around one end or a ⅔ML² for a point mass at the rod's center of mass.