Question

The diameters of the front and the rear wheels of a tractor are 63 cm and 1.54 m respectively. The rear wheel is rotating at `24 6/11` revolutions per minute. Find:
(i) the revolutions per minute made by the front wheel.
(ii) the distance traveled bu the tractor in 40 minutes.

Answer 1

Given the diameter of the front and rear wheels are 63 cm = 0.63 m and 1.54 m respectively,
The radius of the rear wheel = `1.54/2` = 0.77 m.

and radius of the front wheel = `0.63/2` = 0.315 m

Distance traveled by tractor in one revolution of the rear wheel = circumference of the rear wheel
= 2πr
= 2 x `22/7` x 0.77
= 4.84 m

The rear wheel rotates at `24 6/11` revolutions per minute
= `270/11` revolutions per minute

Since in one revolution, the distance traveled by the rear wheel = 4.84 m

So, in `270/11` revolutions, the tractor travels `270/11` x 4.84 = 118.8 m
Let the number of revolutions made by the front wheel be x.

(i) Now, the number of revolutions made by the front wheel in one minute x circumference of the wheel

= the distance traveled by tractor in one minute

⇒ `x xx 2 xx 22/7 xx 0.315 = 118.8`

⇒ `xx = [ 118.8 xx 7 ]/[ 2 xx 22 xx 0.315 ]` = 60

(ii) Distance traveled by tractor in 40 minutes
= number of revolutions made by the rear wheel in 40 minutes
x circumferent of the rear wheel

= `270/11 xx 40 xx 4.84 = 4752` m