The above are the forces on mass due to the inclined plane.
the frictional force will always have the direction opposite to the direction of motion.
Thus for the case of least force on the mass the frictional force will be acting up the incline, as the force applied will be just stopping the box from sliding down. thus we will exert the force upwards:
F + µmgsin30 = mgcos30
on solving we get F=0.
for greatest force which can act on the mass will be in the case we will be trying to move the block up the incline and in that case the frictional force will act downwards.
hence F = mgcos30 + µmgsin30 = 200g N
Angular velocity of the disk is : ? = 60 x 2?/60 = 2? rad/s
Centrifugal force = m?2r = 0.018*4?2*0.08 ~ 0.06N
log10 20 = 1.301
loge 20 = 2.303 * 1.301