Question

A bicycle wheel has diameter 1m. If the bicycle travels 1 km, then the number of revolutions the wheel make is
$(a){\text{ }}\dfrac{1}{\pi }$
$(b){\text{ }}\dfrac{{100}}{\pi }$
$(c){\text{ }}\dfrac{{500}}{\pi }$
$(d){\text{ }}\dfrac{{1000}}{\pi }$

Answer 1

Hint: In the above given question, the diameter of the wheel is used to calculate the circumference of the wheel, then this circumference can be substituted in the equation so formed by the conditions given in the question and on further evaluation, the required solution can be obtained.

Complete step-by-step answer:
Let the number of revolutions of the wheel be $n$.
It is given that the diameter of the bicycle wheel =1 m.
So, the radius of the bicycle wheel$r = \dfrac{1}{2}$.
The distance travelled by the bicycle$ = 1{\text{ km = 1000 m}}$
The circumference of the wheel of the bicycle$ = 2\pi r$
Now, we know that,
$n \times $circumference of wheel= Distance travelled by bicycle
$ \Rightarrow n \times 2\pi \times \dfrac{1}{2} = 1000$
$ \Rightarrow n \times \pi = 1000$
$\therefore n = \dfrac{{1000}}{\pi }$
Therefore, the number of revolutions made by a wheel is$\dfrac{{1000}}{\pi }$.
Hence, the correct answer is the option$(d)$.

Note: Here, the distance travelled by the bicycle is already given. Use the fact that the distance travelled by the cycle is equal to the product of the number of revolutions made by the wheel of the bicycle to the circumference of the wheel.