The diameters of the front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that a rear wheel makes to cover the distance which the front wheel covers in 800 revolutions.
Given diameter of front wheel = d = 80 cm
so, Radius of front wheel = r = d/2 = 80/2 = 40 cm
Diameter of rear wheel = D = 2 m = 200 cm
Distance covered by wheel in 1 revolution = Circumference of wheel
⇒ Distance covered by front wheel = 2πr = 2π(40)
⇒ Distance covered by front wheel = 80π
∴ Distance covered by front wheel in 800 revolutions = 80π×800
⇒ Distance covered by front wheel in 800 revolutions = 6400π → eqn1
⇒ Distance covered by rear wheel = 2πR = 2π(100)
⇒ Distance covered by rear wheel = 200π → eqn2
Let the number of revolutions made by rear wheel to cover 6400π cm be “x”
∴ (x)×200π = 6400π (from eqn1 and eqn2)
⟹ x = 64000/200
⇒ x = 320
Number of revolution made by rear wheel to cover the distance covered by front wheel in 800 revolutions is 320.