Question

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 is 800 revolutions.

Answer 1

Radius of the front wheel = $40\mathrm{cm}=\frac{2}{5}\mathrm{m}$

Circumference of the front wheel = $\left(2\mathrm{\pi }\times \frac{2}{5}\right)\mathrm{m}=\frac{4\mathrm{\pi }}{5}\mathrm{m}$

Distance covered by the front wheel in 800 revolutions = $\left(\frac{4\mathrm{\pi }}{5}\times 800\right)\mathrm{m}=\left(640\mathrm{\pi }\right)\mathrm{m}$
Radius of the rear wheel = 1 m
Circumference of the rear wheel = $\left(2\mathrm{\pi }\times 1\right)=2\mathrm{\pi }\mathrm{m}$

∴ Required number of revolutions = $\frac{\mathrm{Distance}\mathrm{covered}\mathrm{by}\mathrm{the}\mathrm{front}\mathrm{wheel}\mathrm{in}800\mathrm{revolutions}}{\mathrm{Circumference}\mathrm{of}\mathrm{the}\mathrm{rear}\mathrm{wheel}}$
$$\begin{gathered} =\frac{640\mathrm{\pi }}{2\mathrm{\pi }} \\ =320 \end{gathered}$$