Answer :
Final answer:
The pulley moves 400 revolutions. Therefore the correct option is b.
Explanation:
To find the number of revolutions the pulley moves, we need to calculate the angular displacement. The angular displacement can be calculated using the formula:
Angular Displacement = (angular velocity) * (time)
Since the pulley is brought to rest, the final angular velocity is 0. The initial angular velocity can be calculated using the formula:
Initial Angular Velocity = (initial angular velocity) - (angular acceleration * time)
Since the pulley is rotating at a constant speed, the angular acceleration is 0. So, the initial angular velocity is equal to the angular velocity.
Let's calculate the initial angular velocity:
Angular velocity = (2π * r) * (rpm / 60)
where r is the radius of the pulley and rpm is the number of revolutions per minute.
Substituting the values:
Angular velocity = (2π * 0.5) * (600 / 60) = π * 10 rad/s
Now, substituting the values into the formula:
Angular Displacement = (π * 10) * 80 = 800π rad
Since there are 2π radians in one revolution, the number of revolutions the pulley moves can be calculated as:
Number of revolutions = (800π) / (2π) = 400
Therefore, the pulley moves 400 revolutions.
