Answer
Please see the work below.
Work Step by Step
(a) We know that the solid disk swings from right to left and the magnetic field is into the page. Thus, the induced current should produce the induced magnetic field which is opposite to the field -- that is, the field must be directed out of the page. We conclude that the induced current is in counter-clockwise direction.
(b) We know that the best explanation is option (II) -- that is, the induced current is counter clockwise since this produces a field within the disk in the same direction as the magnetic field that produces the current.
