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The wheel of a motorcycle, 70cm in diameter, makes 40 revolutions every 10 seconds. What is the speed of the motorcycle in km/hr?
(A) 22.32
(B) 27.68
(C) 31.68
(D) 36.24

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Last updated date: 19th Apr 2024
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Answer
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Hint First calculate the distance covered by the motorcycle in given time using the following formula
${\text{Distance covered = Number of revolutions x Circumference of the wheel}}$
Circumference of the wheel = Circumference of the circle =$\pi {R^2}$
Where, R = Radius of the wheel
Next use the relation between speed, time and distance to get the answer.

Complete step by step solution
We know distance covered by the wheel is given by
${\text{Distance covered = Number of revolutions x Circumference of the wheel}}$
Circumference of the wheel = Circumference of the circle =$\pi {R^2}$
Where, R = Radius of the wheel
According to the problem
R = \[{\text{70/2}}\] = 35 cm (we divided 70 by 2 because 70 is the diameter of the wheel)
Number of revolutions = 40
Time = 10 second
$\therefore $Distance covered in 40 second = $40\times\pi \times{35^2}$cm
                                        = 8800 cm
                                        = 88 m
Or, Distance covered in 1 second = \[{\text{88/10}}\] = 8.8 m
Now,
$Speed = \dfrac{{Dis\tan ce}}{{Time}}$
Or, $Speed = \dfrac{{8.8}}{1}$ m/sec = \[{\text{8}}{\text{.8 m/sec}}\]
Again, to convert m/sec to km/hr we multiply m/sec with \[{\text{18/5}}{\text{.}}\]
$\therefore $ Speed = $8.8\times\dfrac{{18}}{5}$ km/hr =\[{\text{31}}{\text{.68 km/hr}}{\text{.}}\]

(Option C)

Note: We are using the formula of circumference of the circle because wheels are in the form of a circle. In 1 revolution the motorcycle covers the distance equal to the circumference of the wheel. In the above question the value of π is 3.14 as the question does not mention its value however in case it is mentioned in the question used that value only. To convert m/sec to km/hr multiply m/sec with 18/5 and to convert km/hr to m/sec multiply km/hr with 5/18. You may remember this by remembering 18>5 is similar to km>m so in case we are going to km/hr from m/sec 18 will be in the numerator and 5 in denominator and vice-versa.