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A mountain bike has a sprocket and chain drive system designed to adjust the force needed by an operator. The system consists of one sprocket driven by the pedals with a diameter of 10 inches, and a second on the back wheel with a diameter of 6.5 inches. If the operator is pedaling at 40 rpm, what is the output speed on the back tire? O 35.72 rpm 0 26 rpm 0 53.24 rpm 0 61.53 rpm​

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Answer:

B. 26 rpm

Explanation:

The sprocket has a diameter of 10 in

The back wheel has a diameter of 6.5 in

One complete revolution formula is : 2πr -------where r is radius

For the sprocket , one revolution = π * D where D=2r

π * 10 = 31.4 in

For the back wheel, one revolution = π* 6.5 = 20.42 in

The pedaling rate is : 40 rpm

Finding the ratio of revolutions between the sprocket and the back tire.

In one revolution; the sprocket covers 31.4 in while the back tire covers 20.42 in so the ratio is;

20.42/ 31.4 = 0.65

So if the speed in the sprocket is 40 rpm then that in the back tire will be;

40 * 0.65 = 26 rpm

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