Answer
(a) $I = 0.010~kg~m^2$
(b) $I = 0.030~kg~m^2$
Work Step by Step
(a) We can find the moment of inertia of the disk for a perpendicular axis through the center.
$I = \frac{1}{2}MR^2$
$I = \frac{1}{2}(2.0~kg)(0.10~m)^2$
$I = 0.010~kg~m^2$
(b) We can use the parallel axis theorem to find the moment of inertia about an axis that is through the edge of the disk. Note that the distance $d$ from the center of mass to the edge of the disk is 10 cm.
$I = I_{cm}+Md^2$
$I = 0.010~kg~m^2+(2.0~kg)(0.10~m)^2$
$I = 0.030~kg~m^2$
