In covering a distance \(s\) metres, a circular wheel of radius \(r\) metres makes \(\dfrac{s}{2\pi r}\) revolutions. Is this statement true? Why?
Step 1: A wheel is circular. When it makes one complete turn (one revolution), the distance it moves forward is equal to the circumference of the wheel.
Step 2: The circumference of a circle is given by the formula:
\( C = 2\pi r \)
where \(r\) is the radius of the wheel (in metres, SI unit of length).
Step 3: So, in one revolution, the wheel covers a distance of \(2\pi r\) metres.
Step 4: If the wheel covers a total distance of \(s\) metres, then the number of revolutions is:
\( \text{Number of revolutions} = \dfrac{\text{Total distance}}{\text{Distance per revolution}} \)
\( = \dfrac{s}{2\pi r} \)
Step 5: This is exactly the same as given in the question. Therefore, the statement is True.