The small ball shown in the figure is bounded to move in the vertical slot due to the rotation of the arm and has a mass of 1.5 kg. Evaluate the reaction of the slot on the ball when q = 30⁰. The constant angular velocity of the rod is 4 rad/s. The ball contacts only one side at any instant.

a. 32.1 N in the positive x-direction
b. 32.1 N in the negative x-direction
c. 16.1 N in the positive x-direction
d. 16.1 N in the negative x-direction

Considering the forces acting on the ball, we have

(F + m a_q) cos q+ m a_r sin q = m g

solving the above equation by substituting the required values we get
F = -16.1 N

N = (F + m a_q) sin q - m a_r cos q
solving the above equation gives N = -32.1 N

The reaction of the slot on the ball is 32.1 N in the negative x-direction.