A 100-Kg Rod Has a Varying Linear Density That Is Symmetric

Multiple Choice

A 10.0-kg rod has a varying linear density that is symmetric about the midpoint of the rod. The moment of inertia about an axis perpendicular to the rod that passes through the rod 30.0 cm from its midpoint is 5.00 kg∙m². What is the moment of inertia about an axis perpendicular to the rod that passes through the rod 20.0 cm from its midpoint?

A) 7.50 kg∙m²
B) 4.50 kg∙m²
C) 5.10 kg∙m²
D) 4.90 kg∙m²
E) Answer depends on whether the new axis is on the same side of the midpoint as the 30.0 cm distant axis or if its on the opposite side of the midpoint.