Question

The diameter of a bullock cart wheel is \[\dfrac{14}{11}\] meters. This wheel makes 10 complete revolutions per minute. What would be the speed of the cart in kilometers per hour?
A) 4.8
B) 9.6
C) 8.8
D) 2.4

Answer 1

HINT:- Before solving this question, we must know about the diameter, radius and circumference of a circle.
DIAMETER: The diameter of a circle is the length of the line through the center that touches two points on the edge of the circle.
RADIUS: The radius of a circle is any of the line segments from its center to its perimeter (circumference).
CIRCUMFERENCE: The distance around the edge of a circle is called its circumference. The circumference of a circle is just like its perimeter.
Let us now know about the formula to calculate the circumference of a circle.
CIRCUMFERENCE: \[2\pi r\]
Where, ‘r’ refers to the radius of the circle.

Complete step-by-step answer:
According to the question, the diameter of the wheel of the bullock cart is \[\dfrac{14}{11}\] meter.
So, the radius of the circle will be \[\dfrac{14}{11}\] ÷ 2 = \[\dfrac{7}{11}\] .
Now, we will be calculating the circumference of the wheel by the formula provided in the hint.
Circumference: \[2\pi r\]
Circumference of the wheel = \[2\pi r\]
                                                   = \[2\ \times \ \dfrac{22}{7}\ \times \ \dfrac{7}{11}\]
                                                   = \[2\ \times \ 2\ =\ 4\]
Therefore, the circumference of the wheel is 4 meter.
According to the question, the number of revolutions completed by the wheel is 10.
Therefore, the distance travelled by the wheel = \[\text{Circumference} \times \text{ No. of revolutions}\]
                                                                                     = \[4\ \times \ 10\ =\ 40\]
So, the distance travelled by the wheel in 10 revolutions is 40 meter.
So, the speed of the wheel can be calculated as follows.
\[Speed=\dfrac{\text{Distance}}{\text{Time}}\]
\[Speed\ =\ \dfrac{40}{1}\]
We know that 1 minute = 60 seconds.
Therefore, \[Speed\ =\ \dfrac{40}{1}\] can also be written as follows:-
\[Speed\ =\ \dfrac{40}{60}\ =\ \dfrac{2}{3}\]
\[Speed\ =\ \dfrac{2}{3}\ m/s\]
Now to convert this into km/h, we need to multiply this fraction by \[\dfrac{18}{5}\] .
\[\dfrac{2}{3}\ \times \ \dfrac{18}{5}\ =\ \dfrac{12}{5}\ =\ 2.4\]
Hence, the speed of the wheel is 2.4 km/hr.
Therefore, the correct option for this question is (D) 2.4 km/hr.

NOTE:- We must remember that when we need to convert ‘kilometer per hour’, i.e. km/hr into ‘meter per second’, i.e. m/s, we multiply it by \[\dfrac{5}{18}\] .
Also, when we need to convert ‘meter per second’, i.e. m/s into ‘kilometer per hour’, i.e. km/hr, we multiply it by \[\dfrac{18}{5}\] .
This makes our calculation easier and shorter.
One must do all the calculations in this question very carefully. If the student makes any mistake in the calculations, then the answer so obtained will not be correct.
Also not only in this question, the students must be very careful while solving any such questions as if there is any mistake in the calculus, then the answer can come out to be wrong.