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



First of all, don't forget that the sun is 400 times farther from us than the moon is. That fact alone tells us that anything on the earth is attracted to each kilogram of the moon with a force that's 160,000 times stronger than the force that attracts it to each kilogram of the Sun.
But more to your point ... The tides ARE greatly influenced by the sun. That's why tides are considerably higher at New Moon, when the sun and moon are both pulling in the same direction.
This is called an organ. Examples of organs are: your heart, brain, lungs, liver, stomach etc.