Final answer:
The moment of inertia of a solid disk about an axis through its center of mass is I = 1/2 MR². This is also the answer to the question, which is to determine the moment of inertia of the wheel given its specific weight. Option A is correct.
Step-by-step explanation:
The question requires determining the moment of inertia (I) of a wheel about an axis passing through its center of mass. The answers provided are in the form of fractions of the product of mass (M) and the square of the radius (R²).
When dealing with a solid disk, the formula for the moment of inertia about the axis through the center of mass (perpendicular to the plane of the disk) is I = 1/2 MR². This formula is derived from the integration of the mass distribution across the disk's volume and is a standard result in physics for a uniform solid disk.
Given that, the correct answer would be option (a) I = 1/2 MR².
In a situation where a child is considered as a point mass on a merry-go-round, the moment of inertia of the child (Ic) would be calculated as Ic = MR², using the mass of the child and the square of their distance from the rotation axis.
For example, if a child's mass is 18.0 kg and the distance from the axis is 1.25 m, then Ic = (18.0 kg)(1.25 m)² = 28.13 kg · m², which would then be added to the merry-go-round's own moment of inertia to find the total moment of inertia.