Wheel speed from revolutions: A vehicle’s wheel has radius 70 cm. It completes 10 revolutions in 5 seconds. Find the vehicle’s speed in km/h (assume no slipping).

Introduction / Context:
Converting rotational motion to linear speed is routine in aptitude and physics-based word problems. The core is relating revolutions per second to distance per second using the wheel circumference, then converting units to km/h.

Given Data / Assumptions:

• Radius r = 70 cm = 0.7 m
• Revolutions: 10 in 5 s → 2 rev/s
• No slip between wheel and road (distance = circumference * revolutions)

Concept / Approach:
Circumference C = 2 * π * r. Linear speed v (m/s) = rev/s * C. Convert m/s to km/h by multiplying by 3.6.

Step-by-Step Solution:
C = 2 * π * 0.7 = 1.4π m ≈ 4.398 mv = 2 * 1.4π ≈ 8.796 m/sConvert to km/h: 8.796 * 3.6 ≈ 31.67 km/h ≈ 31.68 km/hr.

Verification / Alternative check:
Using π ≈ 22/7 gives C = 1.4 * 22/7 = 4.4 m; speed = 2 * 4.4 = 8.8 m/s; 8.8 * 3.6 = 31.68 km/hr., matching the selected option exactly.

Why Other Options Are Wrong:
29.46 and 28.80 are underestimates; 36.25 and 32.72 do not arise from any reasonable π approximation with the given data.

Common Pitfalls:
Forgetting the 3.6 factor, confusing diameter with radius, or using π inconsistently can produce close-but-wrong values.

Final Answer:
31.68 km/hr.