Question

The diameter of every wheel of a car is 63 cm. How much distance will the car move during 2000 revolutions of its wheels?

Answer 1

Hint: When a wheel rolls on the ground without slipping, the distance covered by the wheel in one complete revolution is equal to the circumference of the wheel. The circumference of a circle is given as $ C=2\pi r $ , r is the radius of the circle.
Formula used:
  $ C=2\pi r $
  $ r=\dfrac{d}{2} $

Complete step-by-step answer:
It is given that the diameter of the wheels of a car is equal to 63 cm. We are supposed to find the distance moved by the car when each of its wheels completes 2000 number of revolutions.
Let us assume that all the four wheels of the car are rotating without slipping on the ground. When a wheel rolls on the ground without slipping, the distance covered by the wheel in one complete revolution is equal to the circumference of the wheel.
Therefore, let us find the circumference of the wheel.
The shape of a wheel is a circle. The circumference of a circle is given as $ C=2\pi r $ ….. (i), r is the radius of the circle.
And the radius of a circle is equal to half of its diameter (d).
i.e. $ r=\dfrac{d}{2} $
Substitute the value of r in (i).
  $ \Rightarrow C=2\pi \dfrac{d}{2}=\pi d $ .
It is given that the diameter of each wheel is 63 cm.
  $ \Rightarrow C=\pi (63\;cm)=198\;cm $ .
This means that the car moves forward by a distance of 198 cm when its wheels complete one revolution.
 Therefore, in 2000 revolutions, the car will move a distance of $ 2000\times 198cm=396000cm=3.96\;km $ .
So, the correct answer is “3.96 km”.

Note: The condition that all the wheels of the car are rolling without slipping is necessary. If the wheels slip, distance moved by the car wheel will not be equal to the circumference of the wheels.
For example, when we apply breaks with driving, and the car skids. In this case, the wheels do not roll but still the car moves forward.