Question

A cyclist goes around a circular track once every, $2min$. If the radius of the circular track is, $105m$ then the speed of the cyclist will be

• A. $5m{s}^{-1}$
• B. $3.5m{s}^{-1}$
• C. $5.5m{s}^{-1}$
• D. $3m{s}^{-1}$

Answer 1

The correct option is C

$5.5m{s}^{-1}$

Step 1: Given and to find

The radius of the circular track, $r=105m$

Time is taken,$t=2min=2\times 60=120seconds$

And we need to find speed.

Step 2: Formula for speed and circumference of the circle

1. The radius of the circle is required to calculate the circumference
2. To find the diameter, divide the radius by two.
3. Multiply the result by π, or 3.14 for an estimation. That's all; you calculate the circle's circumference.
4. Then, the Circumference of the circle = 2πr…….(I)
5. Also, speed is defined as distance per unit of time,i.e $Speed=\frac{Dis\tan ce}{Time}$……..(ii)

Step 3: Finding the speed of the cyclist

1. Putting all given the values in equation (I), we get the Circumference of the circular track $=2\times \frac{22}{7}\times 105$ $=660m=dis\tan ce$
2. Then we know that the formula of speed putting all values in eq. (ii) then we get

$\Rightarrow Speed=\frac{660}{120}\Rightarrow Speed=5.5m/s$

3. Hence, the speed of the cyclist will be $5.5m/s.$

Thus, Option (C) $5.5m/s$ is the correct option.