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.

Answer 1

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.