Answer:
Part a)

Part b)

Part c)

Part d)

Explanation:
Part a)
While bucket is falling downwards we have force equation of the bucket given as

for uniform cylinder we will have

so we have


now we have




now we have


Part b)
speed of the bucket can be found using kinematics
so we have



Part c)
now in order to find the time of fall we can use another equation



Part d)
as we know that cylinder is at rest and not moving downwards
so here we can use force balance



Type motion examples and subtypes
electromagnetic radiation disturbance propagating through electric and magnetic fields (classical physics) or the motion of photons (modern physics) radio waves, microwaves, infrared, light, ultraviolet, x-rays, gamma rays
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Answer:
Kinetic energy of the brick is 26.4 Joule