# CLASS-9CIRCUMFERENCE & AREA OF CIRCLE - ROTATION MADE BY A WHEEL

(i)  Distance moved by a wheel in 1 revolution = Circumference of the Wheel

(ii) Number of rotations made by a wheel in unit time

Distance moved by it in unit time

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Circumference of the wheel

Example.1)  The wheel of a cart is making 6 revolutions per second if the diameter of the wheel is 84 cm, fin its speed in km/hr. give your answer correct to nearest km.

Ans.) (In that case we have to understand the logic behind it. Wheel is moving on the road as per his circumference) We have to find out the circumference of the wheel. Diameter of the wheel 84 cm, so the radius of the wheel r = 98/2 cm                                                                                                                                                 = 49 cm

22

Circumference of the wheel = 2πr2 X ------ X 49

7

= (2 X 22 X 7) = 308 cm

So, distance moved by the wheel in 1 revolution = 308 cm

Distance moved by the wheel in 6 revolution per seconds = (308 X 6)                                                                                                                                                = 1848 cm

So, distance moved by the wheel in 1 second is 1848 cm.

As we know that, 1 minute = 60 seconds

1 hour = 60 minutes

1 hour = 60 minutes X 60 seconds = 3600 seconds

So, distance moved by wheel in 1 hour = 3600 seconds X 1848 cm

= 6652800 cm/hr

As, we know that 100 cm = 1 meter

And, 1000 meter = 1 km

So, 1 km = 100000 cm

6652800 cm

So, the speed of the cart is = --------------- =  66.52 km/hr

100000 seconds

Hence the speed of the cart, correct to nearest km/hr is 67 km/hr.    (Ans.)

Example.2) The diameter of the driving wheel of a bus is 140 cm. how many revolution must the wheel make in order to keep a speed of 66 km/hr.

Ans.) (In that case we have to understand the logic behind it. Wheel is moving on the road as per his circumference) We have to find out the circumference of the wheel.

Diameter of the wheel is 140 cm, so the radius of of the wheel is 140 cm/2 = 70 cm

22

The circumference of the wheel is 2πr2 X ------- X 70

7

=  (2 X 22 X 10) =  440 cm

The wheel need to revolute to get journey 66 km 6600000 cm

6600000

So, number of revolution should be = ------------ = 15000

440

Per minute revolution must be = 15000/60

= 250 revolution per minute.    (Ans.)

Example.3) A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. Given that the bucket ascending in 1 minutes 28 seconds with a uniform speed of 1.1 meter/seconds, calculate the number of complete revolutions the wheel makes in raising the bucket.

Ans.) Time taken by bucket to ascend = 1 min 28 sec = 88 seconds

Speed = 1.1 meter/seconds

Length of the rope = Distance covered by bucket to ascend

= (1.1 X 88) meter

= (1.1 X 88 X 100) cm = 9680 cm

Radius of the wheel = 77/2 cm

22         77

Circumference of the wheel = 2πr = (2 X ------ X ------) cm

7          2

242 cm

Length of the rope

Number of revolutions = ---------------------------

Circumference of the wheel

9680

= ---------- =  40

242

Hence, the wheel makes 40 revolution to raise the bucket.   (Ans.)