Answer:
The leverage or mechanical advantage of pulleys is less obvious, but you can "gang" multiple pulleys together into two sets (blocks) and run the ropes back and forth between the two sets to increase the number of lengths of rope running between them. One end of the rope is connected (fixed) to one of the blocks, and you get to pull on the other end after it is passed back and forth between the blocks of pulleys. This is sometimes called a block and tackle arrangement. With a hook on each side of the block set, you can move a heavy load much like levers do, by multiplying the force. You have to pull more rope just like you have to move a lever more on one side of the fulcrum as compared to the other. When you get all the rope pulled out that you can, you can not move the load anymore because you have become "two-blocked" which means the two blocks are together. Credits to: Moin Khan
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


