Answer:
The velocity of the bucket is 3.83 m/s.
Step-by-step explanation:
Given that,
Mass of bucket = 2.0 kg
Mass of cylinder =4.0 kg
Distance = 1.50 m
We need to calculate the speed
Using equation of motion

Put the value into the formula


We need to calculate the tension
Using equilibrium equation

....(I)
Put the value into the formula

Now, using formula of tension
...(II)
Moment of inertia of cylinder

Angular velocity of cylinder is

Put the value of angular velocity in equation (II)


Put the value of tension in equation (I)

Put the value into the formula



Put the value of acceleration in equation of motion



Hence, The velocity of the bucket is 3.83 m/s.