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When a bicycle is moving at a speed of 3 km/hr the circular tire completes 500 full rotations in 17 min. 36 sec. When the circular tire gets detached from the moving bicycle and continues to run freely for 2 minutes 56 seconds at a speed of 0.9 km/hr before coming to a halt, then how many full rotations will it complete before coming to halt?

When a bicycle is moving at a speed of 3 km/hr the circular tire completes 500 full rotations in 17 min. 36 sec. When the circular tire gets detached from the moving bicycle and continues to run freely for 2 minutes 56 seconds at a speed of 0.9 km/hr before coming to a halt, then how many full rotations will it complete before coming to halt? Correct Answer 25

Given:

Bicycle is moving at a speed of 3 km/hr

 Circular tire completes 500 full rotations in 17 min 36 sec

Speed of bicycle when moving freely = 0.9 km/hr

Time take to come to halt when moving freely = 2 minutes 56 seconds

Formula used:

Speed = Distance/Time

Calculation:

When the bicycle is moving,

Speed of bicycle = 3 km/hr = 3 × 5/18 = (5/6) m/sec.

Time taken to cover 500 rotations = 17 min 36 sec = 17 × 60 + 36 = 1056 sec

⇒ Total distance covered in 500 rotations = Speed × Time = (5/6) × 1056 = 880 m

⇒ Distance covered in 1 rotation = 880/500 = 1.76 m

Now,

When the tire is detached from the bicycle,

Speed of tire = 0.9 km/hr. = 0.9 × 5/18 = 1/4 m/sec.

Time taken by tire to come to halt = 2 min 56 sec = 2 × 60 + 56 = 176 sec 

⇒ Total distance covered by tire before halting = (1/4) × 176 = 44 m 

∴ No. of full rotations made by tire before halting = Total distance covered/Distance covered in 1 rotation = 44/1.76 = 25

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