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Question
The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.
Solution
According to the question,
Diameter of front wheels = d1 = 80 cm
Diameter of rear wheels = d2 = 2 m = 200 cm
Let r1 be the radius of the front wheels = `80/2` = 40 cm
Let r2 be the radius of the rear wheels = `200/2` = 100 cm
Now, Circumference of the front wheels = 2πr
= `2 xx 22/7 xx 40`
= `1760/7` cm
Circumference of the rear wheels = 2πr
= `2 xx 22/7 × 100`
= `4400/7` cm
No. of revolutions made by the front wheel = 1400
∴ Distance covered by the front wheel
= `1400 xx 1760/7`
= 352000 cm
Number of revolutions made by rear wheel in covering a distance in which the front wheel makes 1400 revolutions
= `"Distance covered by front wheel"/"Circumference of the rear wheel"`
= `352000/(4400/7)`
= `(352000 xx 7)/4400`
= 560 revolutions.
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