A square hole is centered in and extends through the aluminum machine component shown. Determine (a) the value of a for which the mass moment of inertia of the component with respect to the axis AAʹ, which bisects the top surface of the hole, is maximum, (b) the corresponding values of the mass moment of inertia and the radius of gyration with respect to the axis AAʹ. (The specific weight of aluminum is 0.100 lb/in3.)

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4.2 in. 15 in 4.2 in