Question

In covering a distance $s$ metres, a circular wheel of radius $r$ metres makes $\frac{s}{2\mathrm{\pi r}}$ revolutions. Is this statement true? Why?

Answer 1

Calculate the number of revolutions.

The distance travelled by a circular wheel of $\mathrm{r}\mathrm{units}$ radius in one revolution is equal to the circumference of the circle which is equal to $2\mathrm{\pi r}$.

So, the number of revolutions completed in $2\mathrm{\pi r}\mathrm{units}$ distance $=1.$

Number of revolutions completed in $1\mathrm{unit}$ distance $=\left(\frac{1}{2\mathrm{\pi r}}\right)$

Number of revolutions completed in $s\mathrm{units}$ distance

$$\begin{gathered} =\left(\frac{1}{2\mathrm{\pi r}}\right)\times s \\ =\frac{s}{2\mathrm{\pi r}} \end{gathered}$$

Hence, the given statement is True.