Question

A car travels 1 km distance in which each wheel of the car makes 450 complete rotations. Find the radius of the wheels of the car.

Answer 1

Hint: Assume that the radius of a wheel of the car is r. Find the distance covered in one rotation of the wheel in terms of r. Hence find the distance covered in 450 rotations of a wheel of the car. Equate this distance with $2\pi r$. and hence form an equation in r, Solve for r. The value of r will be the radius of a wheel of the car.

Complete step by step answer:
Let r be the radius of the wheels of the car in metres.
We have distance covered by the car in one complete rotation of its wheels = circumference of the wheel.
We know that the circumference of a circle of radius r $=2\pi r$.
Hence the distance covered by the car in one complete rotation of its wheels $=2\pi r$.
Hence the distance covered in 450 complete revolutions of its wheels $=450\times 2\pi r=900\pi r$.
But, given that the car covers 1 km in 450 rotations of its wheels.
Hence, we have
$900\pi r=1000$
Hence,
$r=\dfrac{1000}{900\pi }=\dfrac{10}{9\pi }=0.35$ metres.
Hence the radius of the wheels of the car = 0.35m.

Note: In the above solution, we have assumed that the car rolls, without slipping. When a circular object rolls without slipping, the distance covered in one revolution of the object is equal to the circumference of the circle (Rolling surface).