The right answer is (b) mω02a
Explanation:
The frame of reference is rotating with a uniform angular speed ω0, so it has an acceleration towards the center and it is a non-inertial plane. To apply Newton's Laws in this frame we apply a pseudo force equal to mω0²a to the particle but opposite to the direction of the acceleration of the frame. This pseudo force is the centrifugal force on the particle.