Question

A flat belt pulley has a circumference of 40 cms and turns at 60 rpm. It rotates another pulley of 1.2 meters circumference through a belt having 7.2 meters in length. If the driven pulley has revolved 600 times, what is the time the driver pulley rotated?

• A. 20 minutes
• B. 30 minutes
• C. 40 minutes
• D. 120 minutes

Hint:

In belt drives, always compare \textit{linear distance} travelled by the belt, not rpm directly.

Answer 1

The Correct Option is B

Step 1: Understanding pulley motion.
For belt-driven systems, the length of belt passed over both pulleys must match. Therefore, the linear distance travelled by each pulley is the key to solving the problem.

Step 2: Calculate belt distance for 600 revolutions of the driven pulley.
Driven pulley circumference = 1.2 m.
Revolutions = 600.
\[ \text{Total belt travelled} = 600 \times 1.2 = 720 \text{ m} \]
Step 3: Find revolutions of driver pulley.
Driver pulley circumference = 40 cm = 0.40 m.
\[ \text{Driver revs} = \frac{720}{0.40} = 1800 \text{ revolutions} \]
Step 4: Find time at 60 rpm.
\[ \text{Time} = \frac{1800}{60} = 30 \text{ minutes} \]
Step 5: Conclusion.
Thus, the driver pulley must rotate for 30 minutes, so the correct answer is (B).