Final answer:
The moment of inertia of the merry-go-round can be calculated by summing the moments of inertia of both the merry-go-round and the child. In this case, the formula for the moment of inertia of the child is Ic = MR², and the formula for the moment of inertia of the merry-go-round is Im = 1mmr². By substituting known values into the formulas, the total moment of inertia can be calculated. In this case, option (B) with a moment of inertia of 254.71 kg·m² is the closest to the calculated value.
Step-by-step explanation:
The moment of inertia of the merry-go-round can be calculated by summing the moments of inertia of both the merry-go-round and the child. In this case, the formula for the moment of inertia of the child is Ic = MR², where M is the mass of the child and R is the distance of the child from the axis. The moment of inertia of the merry-go-round can be given as Im = 1mmr², where m is the mass of the merry-go-round and r is its radius. By substituting known values into the formulas, the total moment of inertia can be calculated.
In the given options, it seems that option (B) with a moment of inertia of 254.71 kg·m² is the closest to the calculated value.