The wheel of a motorcycle is 70 cm in diameter. It makes 40 revolutions in every 10 seconds. Find the speed of the motorcycle in km/hr (assume pi = 22/7 for exact calculation).

Introduction / Context:
This question tests the link between rotational motion and linear speed. Each wheel revolution moves the motorcycle forward by one circumference of the wheel. By multiplying circumference by revolutions per second, you get linear speed in m/s. Finally, convert m/s to km/hr using the standard factor (multiply by 18/5). The key is careful unit conversion from cm to m and seconds to hours.

Given Data / Assumptions:

• Diameter d = 70 cm
• Revolutions = 40 in 10 s
• pi = 22/7
• 1 m = 100 cm
• m/s to km/hr: multiply by 18/5

Concept / Approach:
Distance per revolution = circumference = pi*d. Revolutions per second = 40/10. Speed (cm/s) = circumference * rev/s. Convert to m/s, then to km/hr.

Step-by-Step Solution:
Circumference = pi*d = (22/7)*70 = 220 cm per revolutionRevolutions per second = 40/10 = 4 rev/sSpeed = 220*4 = 880 cm/sConvert to m/s: 880 cm/s = 880/100 = 8.8 m/sConvert to km/hr: 8.8*(18/5) = 8.8*3.6 = 31.68 km/hr

Verification / Alternative check:
In 1 second, the wheel makes 4 revolutions, so it travels 4 circumferences = 4*2.2 m = 8.8 m, matching 8.8 m/s. Multiplying by 3.6 gives 31.68 km/hr, which is a realistic low-to-moderate speed for such rotation rate.

Why Other Options Are Wrong:
13.68 results from incorrect rev/s (using 40/30 or similar). 41.68 and 45.68 come from circumference miscalculation or using pi=3.14 inconsistently with cm-to-m conversion. 28.80 often comes from using 3.2 instead of 3.6 as the conversion factor.

Common Pitfalls:
Forgetting to divide revolutions by time to get rev/s. Not converting cm to m. Using the wrong conversion factor to km/hr. Using radius instead of diameter in circumference formula.

Final Answer:
31.68 km/hr