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Question

Two wheels of radii r1 and r2 and circumferences c1 and c2 respectively. Cover the same distance in same time. If in that time, they complete n1 and n2 revolutions respectively.
Prove that n2n1 = r1r2 = c1c2

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Solution

Radius of the 1st wheel = r1
Radius of the 2nd wheel = r2
Circumference of the 1st wheel = c1
Circumference of the 2nd wheel = c2
Number of revolution taken by the 1st wheel = n1
Number of revolution taken by the 2nd wheel = n2
Total distance covered by the 1st wheel = n1×c1
Total distance covered by the 2nd wheel = n2×c2
Total distance covered by the 1st wheel = total distance covered by the 2nd wheel
n1×c1= n2×c2 c1c2 = n1n2 ......(1)c1c2= 2πr12πr2c1c2= r1r2 .......(2)

From (1) and (2), we get,:

c1c2= r1r2 = n1n2

Hence, proved.

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