Question

A wheel bicycle has inner diameter $50cm$ and thickness $10cm$ . What is the speed of the bicycle if it makes a $10$ revolution in $5$ seconds?
A. $5.5m/s$
B. $4.4m/s$
C. $3.3m/s$
D. $2.2m/s$

Answer 1

Hint: We have been given a wheel whose diameter and thickness is given along with the revolution it makes in a certain time. For finding what the speed of the wheel is, firstly we will find the distance travelled by the wheel in one round. Then we will find the revolution made in one second. Finally by using the speed formula we will get our desired answer.

Complete step by step answer:
A wheel is given with below dimensions:
Diameter $d=50cm$….$\left(1\right)$
Thickness $t=10cm$…….$\left(2\right)$
So we can draw the wheel as follows:

Now firstly we will find the Distance travelled by the wheel in one round.
As we know distance of a circular shape is calculated as follows:
Distance $d=2\pi r$…..$\left(3\right)$
Where $r=$ radius of the wheel
Formula for finding radius of wheel is given as:
Radius $r={\displaystyle \frac{d}{2}}+t$….$\left(4\right)$
Where $d=$ diameter $t=$ thickness

Substitute values from equation (1) and (2) in equation (4) we get,
$r={\displaystyle \frac{50}{2}}+10$
$\Rightarrow r=25+10$
So we get the radius as:
$r=35cm$
Substitute the above value in equation (3) we get,
$d=2\pi \times 35$
$\Rightarrow d=2\times {\displaystyle \frac{22}{7}}\times 35$
On solving further we get,
$d=220cm$

As we know $1m=100cm$ so
$d=2.2m$
Next it is given that In $5$ second the wheel make $10$ revolution so we can write it as follows:
$5$ Seconds $=10$ revolution
$1$ Seconds $={\displaystyle \frac{10}{5}}$ revolution
Therefore speed of the bicycle will be,
$\Rightarrow {\displaystyle \frac{10}{2}}\times d$
$\Rightarrow 2\times 2.2m/s$
On solving we get,
Speed $=4.4m/s$

Hence option B is correct.

Note: In this type of question it is necessary to visualize the shape of the object given. As we have been provided the thickness of it as well so it means the object is in three-dimension and hence it becomes necessary to find the radius of it accordingly. Speed of any object is the division between the distance travelled by it and the time taken to travel that distance.