Question

The diameter of a driving wheel of a bus is $140cm$. How many revolutions per minute must the wheel make in order to keep a speed of $66kmph$?

Answer 1

Hint: To get the required answer, we need to know the concept behind this problem.

Assume you have a wheel (as shown below) and it is rolled once to complete one circle (1 revolution). 

So, the distance travelled by the wheel is equal to the circumference the wheel (yellow color in the above image.)   

In the given, question we are asked to find revolutions per minute under a given speed. Using diameter, we will find the circumference of the wheel. And use the below formula (in proper units) to get the required answer.

$\text{Number of Revolutions per minute} = \dfrac{\text{Distance covered by the wheel }}{\text{Circumference of the Wheel}}$

Complete step by step solution:
Here, we are given a diameter of the wheel, which is basically a circle , so the diameter of the circle is 140cm.
To find the radius of the circle, we will use the formula $radius=\dfrac{diameter}{2}=\dfrac{140}{2}=70cm$ .

Now, we have to find revolutions per minute made by wheel. So, there is formula to find revolutions given as
$\text{Number of Revolutions per minute} = \dfrac{\text{Distance covered by the wheel }}{\text{Circumference of the Wheel}}$ ……………………………..(1)
So, now we will find circumference of wheel given as
$\text{circumference}=2\pi r$
On substituting the value of radius $r$ and $\pi =\dfrac{22}{7}$ we will get,
$\text{circumference}=2\times \dfrac{22}{7}\times 70=440cm$
Now, we will convert 440cm into meters using the relation $1m=100cm$ So, using this we will get circumference as $\dfrac{440}{100}=4.4m$ .
Now, we have speed in kilo-meter so, first we will convert it into meters using the relation $1km=1000m$ . Therefore, 66km will be $66\times 1000=66000m$ per hour. But we want revolution per minute. So, again we will convert hour to minute using the relation $1hour=60\min $ . we get
$ 60\min =66000m $
$  1\min =? $
$\dfrac{66000}{60}=1100m$ per minute.
Now, we will substitute all the values into equation (1) we will get as
$\text{no}\text{. of revolutions=}\dfrac{\text{distance covered}}{\text{circumference}}$
$\text{no}\text{. of revolutions=}\dfrac{1100}{4.4}=\dfrac{11000}{44}=250$
Thus, the wheel will make 250 revolutions per minute with the speed of 66km per hour.

Note: Remember that all the data we are given is in different units i.e. centimetre, kilometre and hour. We have to make it into one single unit i.e. meter and at last convert hour into minute as we asked to find an answer as per minute. Students sometimes forget to convert any one of the units and it results in the wrong answer. Also, mistake happens in writing formula i.e. $\text{no}\text{. of revolutions=}\dfrac{\text{circumference}}{\text{distance covered}}$ instead of using $\text{no}\text{. of revolutions=}\dfrac{\text{distance covered}}{\text{circumference}}$ . So, do not make this silly mistake.