Final answer:
To find the angular acceleration, divide the change in angular velocity (110 rpm) by the change in time (7 minutes), resulting in an angular acceleration of approximately 15.71 rpm/min, which rounds to 15 rpm/min (option a).
Step-by-step explanation:
To calculate the angular acceleration of a machine whose angular speed increases from 0 to 110 rpm in 7 minutes, we can use the formula for angular acceleration which is α = Δω / Δt, where α is the angular acceleration, Δω is the change in angular velocity, and Δt is the change in time. Since the machine starts from rest, the change in angular velocity (Δω) is the final angular velocity, which is 110 rpm. The change in time (Δt) is 7 minutes. To find α in units of rpm/min, divide 110 rpm by 7 min.
α = 110 rpm / 7 min = 15.71 rpm/min
Therefore, the angular acceleration of the machine is approximately 15.71 rpm/min, which can be rounded to 15 rpm/min, which is answer (a).