Question

The diameter of front and rear wheels of a tractor are $80cm$ and $2m$ respectively. Find the number of revolutions that rear wheel will make in covering distance in which the front wheel makes $1400$ revolutions.

Answer 1

Given diameter of front wheels$\left(2r\right)=80cm\Rightarrow r=40cm$

diameter of rear wheels$\left(2r\right)=2m\Rightarrow r=1m=100cm$

In one revolution area covered is $=2\pi r$

$\therefore$ Distance covered by front wheel in $1400$ revolutions $=1400\times 2\pi \left(40\right)$

Let us assume that to cover same distance rear wheel will take $x$ revolutions$=x\times 2\pi \left(100\right)$

As both wheel will cover same distance $\therefore 1400\times 2\pi \left(40\right)=x\times 2\pi \left(100\right)$

$x=\frac{1400\times 40}{100}=560$

That means rear wheel will make $560$ revolutions to cover the required distance.