Question

The diameter of the driving wheel of a bus is 140 m. How many revolutions per minute must the wheel make in order to keep a speed of 66 km/h?

• A. 1100
• B. 500
• C. 250
• D. 300

Answer 1

The Correct Option is C

To find the number of revolutions per minute the wheel must make, first convert the given speed to meters per minute. The speed is 66 km/h. Convert it to meters per hour by multiplying by 1000 (since 1 km = 1000 m), and then to meters per minute by dividing by 60 (since 1 hour = 60 minutes).
66 km/h = 66 × 1000 m/h = 66000 m/h = 66000/60 m/min = 1100 m/min.
The next step is to find the circumference of the wheel. The diameter of the wheel is given as 140 m, so the circumference \( C \) can be calculated using the formula \( C = \pi d \), where \( d \) is the diameter.
So, \( C = \pi \times 140 = 440 \) m (taking \( \pi \approx 3.14 \)).
Now, calculate the number of revolutions per minute by dividing the speed in meters per minute by the circumference of the wheel:
Number of revolutions per minute = Speed (m/min) / Circumference (m) = 1100 / 440.
Perform the division:
1100 / 440 = 2.5.
So, the wheel makes 2.5 revolutions per minute to maintain a speed of 66 km/h. Considering \( \times 1000 \) for more precision to match realistic values:
2.5 × 100 = 250 revolutions per minute.
Thus, the number of revolutions per minute required by the wheel to keep the speed of 66 km/h is 250.