Question

The diameter of the wheel of a bus is 140 cm. How many revolutions per minute must the wheel make in order to move at a speed of 66 km / hr.

Answer 1

Hint:
Here we have to calculate the revolutions made by the bus. For that, we will first find the distance covered by the wheel in one minute as the speed of the bus is given. Then we will find the circumference of the wheel as the diameter of the wheel is given in the question. Then we will calculate the cover by the wheel in one revolution, which will equal to the circumference of the wheel. Then we will divide the distance covered by the wheel in one minute by the distance covered by the wheel in one revolution, which will give the required number of revolutions.

Complete step by step solution:
It is given that:-
Speed of the bus $=66km/hr$
Here it means that the distance covered by the wheel in one hour is 66km.
Now, will calculate the total distance covered by the wheel in one minute (in cm)
Therefore, Total distance covered in 1 min by the wheel $=\dfrac{66\times 1000\times 100}{60}$ { $1km=100000cm$}
On further simplification, we get
Total distance covered in 1 min by the wheel $=110000cm$
Now, we will calculate the circumference of the wheel of diameter 140 cm.
$\text{radius}=\dfrac{\text{diameter}}{2}$
Therefore, Radius (r) $=\dfrac{140cm}{2}=70cm$
We know, Circumference of a circle$=2\pi r$ ; where r is the radius.
Thus, Circumference of the wheel $=2\times \pi \times 70$
Putting value of pi and simplifying it further, we get
Circumference of the wheel $=2\times \dfrac{22}{7}\times 70=440cm$
So the distance covered by the wheel in one revolution will be the same as the circumference of the wheel.
Therefore, Total distance covered in one revolution $=440cm$
Number of revolution per minute $=\dfrac{\text{distance covered by wheel in 1minute}}{\text{distance covered by wheel in one revolution}}$

Putting values of the distance covered by the wheel in one minute and the distance covered by the wheel in one revolution, we get

Number of revolution per minute $=\dfrac{110000}{440}=250$
Hence, the required number of revolutions is 250.

Note:
Here, the number of revolutions made by the wheel per minute means the number of turns made by the wheel in one minute. The total distance covered by the wheel in n number of revolutions will be equal to the n times the circumference of the wheel as the distance covered in one revolution is equal to the value of the circumference of the wheel.