Circular motion – Bus wheel revolutions to maintain 66 km/h: The diameter of the driving wheel of a bus is 140 cm. How many revolutions per minute must the wheel make to keep a speed of 66 km/h?

Introduction / Context:Linear speed at the tyre’s rim equals wheel circumference * revolutions per unit time. Converting units consistently yields rpm (revolutions per minute).

Given Data / Assumptions:

• Diameter = 140 cm ⇒ radius r = 70 cm.
• Speed = 66 km/h.
• π ≈ 22/7 for exact cancellation with 70.

Concept / Approach:Distance per revolution = circumference = 2 * π * r. Convert vehicle speed into cm/min, then divide by circumference to get rpm.

Step-by-Step Solution:

Verification / Alternative check:Back-calc: 250 rev/min * 440 cm = 110,000 cm/min ⇒ 1,100 m/min ⇒ 66 km/h ✔️

Why Other Options Are Wrong:150, 350, 550 do not match the exact circumference-speed ratio after unit conversion.

Common Pitfalls:Unit mistakes (km/h to cm/min), using π = 3.14 with radius 70 cm but forgetting simplification with 22/7.

Final Answer:250