Question

The diameters of the front and rear wheels of a tractor are 80 cm and 2 m respectively. The number of revolutions that the 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: We are given the diameters of front and rear wheel, So firstly we find the radius of both wheels using \[d = 2r\]. Then we find the circumference of both the wheels using \[{\text{C = 2\pi r}}\], Then using the number of revolution of the front-wheel we’ll find the distance traveled by tractor, which is equal to the product of number of revolutions and the circumference of that wheel.
Since both the wheels are of the same body i.e. tractor therefore, both will cover the same distance, and hence equating the distance covered by wheels we’ll get the number of revolutions that the rear wheel will make.

Complete step by step Answer:

Given: The diameter of the front wheels\[\left( {{\text{2r}}} \right){\text{ = 80cm}}\]
So the radius of the front wheels are\[{\text{(r) = 40cm}}\]

and diameter of rear wheels\[\left( {{\text{2r}}} \right){\text{ = 2m}}\]
since 1m=100cm
\[\therefore {\text{2r = 200cm}}\]
, so the radius of the rear wheels\[{\text{(r) = 100cm}}\]


In one revolution area covered is \[{\text{2$\pi$ r}}\] i.e. the circumference of the wheel.

As the radius of the front wheel is 40 cm
∴ Distance is covered by the front wheel in 1400 revolutions =\[1400 \times 2\pi \left( {40} \right)\].

Let us assume that to cover the same distance rear wheel will take x revolutions
∴ Distance is covered by the rear wheel in x revolutions =\[x \times 2\pi \left( {100} \right)\].

As both wheels will cover the same distance
Distance is covered by the front wheel in 1400 revolutions =Distance is covered by the rear wheel in x revolutions

\[ \Rightarrow {\text{1400 $\times 2\pi$ }}\left( {{\text{40}}} \right){\text{ = x $\times 2\pi$ }}\left( {{\text{100}}} \right)\]
Dividing both sides by \[{\text{200$\pi $}}\]
\[ \Rightarrow {\text{x = 14 $\times$ 40}}\]
\[\therefore {\text{x = 560}}\]
That means the rear wheel will make 560 revolutions to cover the required distance.
Hence, the option (c) is correct.

Note: The units given in the problem should be taken into account all the time.
Always convert units of the measurement equivalent as we know that operation (addition or subtraction) can be done only if the units are similar.
Therefore, If the units are not equal or the same, then we might get the wrong result in the end.