Question

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

• A. $11200$
• B. $760$
• C. $560$
• D. $360$

Answer 1

Answer: (C)

$560$

Given: the diameter of the front wheel of a tractor is $d$ =$80$ cm $=$ $0.8$ m

The diameter of the rear wheel of the same tractor is $D=2m$

The front wheel makes $1400$revolutions to cover a distance $x$

To find out: the number of revolutions the rear wheel makes to cover the distance $x$.

Solution:-

The circumference of the front wheel $=\pi d=0.8\times \pi m$

Now a wheel covers a distance $=$ its circumference in one revolution.

$\therefore$ In $1400$ revolutions the front wheel covers $x=1400\times 0.8\pi m=1120\pi m$.

Again the circumference $C$ of the rear wheel $=\pi D=2\times \pi m$

$\therefore$ the number of revolutions $n$ it will make to cover $x$ meter is $n=\frac{x}{C}=\frac{1120\pi }{2\pi }=560m.$