Answer
a). No, moment of inertia does not depend on the center of mass of the body. Moment of inertia depends on the axis of rotation and the distribution of mass around that axis.
b). Moment of inertia cannot be negative because the expression for the same includes the product of mass and square of distance. But negative moment of inertia sometimes comes into picture when there is a negative mass. In all other cases, the moment of inertia cannot be negative.
Work Step by Step
a). No, moment of inertia does not depend on the center of mass of the body. Moment of inertia depends on the axis of rotation and the distribution of mass around that axis.
b). Moment of inertia cannot be negative because the expression for the same includes the product of mass and square of distance. But negative moment of inertia sometimes comes into picture when there is a negative mass. In all other cases, the moment of inertia cannot be negative.