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

Hint:
Here, we will find the distance covered by the front wheel in 1400 revolutions by multiplying its circumference by 1400. Also, by dividing this distance by the circumference of the rear wheel of the tractor, we will find the required number of revolutions.

Formula Used:
Circumference of a circle or circular wheel \[ = 2\pi r\] where \[r\] is the radius of the circle.

Complete step by step solution:
Diameter of front wheel of the tractor \[ = 80{\rm{cm}}\]
Now, Radius is half of diameter. So,
Radius of front wheel of the tractor \[ = \dfrac{{80}}{2} = 40{\rm{cm}}\]
Now, circumference of circular wheel \[ = 2\pi r\]
Substituting \[r = 40\] in the above formula, we get
Circumference of the front wheel of the tractor \[ = 2 \times \dfrac{{22}}{7} \times 40 = \dfrac{{1760}}{7}{\rm{cm}}\]
Now, in 1 revolution, the distance covered by the front wheel of the tractor \[ = \] Circumference of the front wheel of the tractor \[ = \dfrac{{1760}}{7}{\rm{cm}}\]
In 1400 revolutions, the distance covered by the front wheel of the tractor \[ = 1400 \times \dfrac{{1760}}{7}{\rm{cm}}\]
Multiplying the terms, we get
\[ \Rightarrow \]The distance covered by the front wheel of the tractor \[ = 200 \times 1760 = 352000{\rm{cm}}\]
Similarly, Diameter of rear wheel of the tractor \[ = 2{\rm{m}}\]
Now, in 1 m, there are 100 cm. So,
Diameter of rear wheel of the tractor \[ = 2 \times 100 = 200{\rm{cm}}\]
Now, Radius is half of diameter.
Radius of rear wheel of the tractor \[ = \dfrac{{200}}{2} = 100{\rm{cm}}\]
Now, circumference of circular wheel \[ = 2\pi r\]
Substituting \[r = 100\] in the above formula, we get
Circumference of the rear wheel of the tractor \[ = 2 \times \dfrac{{22}}{7} \times 100 = \dfrac{{4400}}{7}{\rm{cm}}\]
Now, the front and the rear wheel of the tractor will move together.
Therefore, when the front wheel has covered a distance of 352000cm
The number of revolutions made by the rear wheel \[ = 352000 \div \dfrac{{4400}}{7}\]
Rewriting the expression, we get
\[ \Rightarrow \] The number of revolutions made by the rear wheel \[ = 352000 \times \dfrac{7}{{4400}}\]
Multiplying the terms, we get
\[ \Rightarrow \] The number of revolutions made by the rear wheel \[ = 560\] revolutions
Therefore, the number of revolutions that the rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions is 560 revolutions.

Hence, option C is the correct answer.

Note:
In this question, the diameter of the front wheel of the tractor is given in centimeters whereas the diameter of the rear wheel is given in meters. If not noticed carefully, then, we could consider both of these as the same unit i.e. either centimeters or meters, hence, making our answer wrong. Thus, it is really important to convert the meters into centimeters or vice-versa, whichever is convenient. Now, a circumference of a circle actually means its perimeter. When the wheel of any vehicle completes one revolution it means that it has covered a full rotation or \[360^\circ \] which is actually the circumference of the circle. Hence, we should know that 1 revolution is always equal to the circumference of the circle.