Question

A cyclist moving on a circular track of radius 100 m completes one revolution in 6 minutes. The average speed and average velocity in one full revolution respectively are given by

• A. $\frac{5\mathrm{\pi }}{12}{\mathrm{ms}}^{-1},0$
• B. $\frac{5\mathrm{\pi }}{9}{\mathrm{ms}}^{-1},0$
• C. $0,\frac{3\mathrm{\pi }}{2}{\mathrm{ms}}^{-1}$
• D. none of these

Answer 1

The correct option is B

$\frac{5\mathrm{\pi }}{9}{\mathrm{ms}}^{-1},0$

Step 1: Given:

1. The radius of the circular track = 100 m.
2. Time taken to complete one revolution = 6 minutes = 360 seconds.

Now we know that;

1. In one complete revolution, it will cover the complete circular track and the circumference of a circular track will be the distance covered.
2. The circumference of a circular track $=2\mathrm{\pi r}$ where r is the radius of the circular track.

Step 2: Finding distance covered in one complete revolution :

So, the distance covered in one complete revolution is given by;

$$\begin{gathered} Dis\tan ce=2\mathrm{\pi r} \\ Dis\tan ce=2\mathrm{\pi }\times 100 \\ Dis\tan ce=200\mathrm{\pi }\mathrm{meters}. \end{gathered}$$

Now,

1. If a cyclist is completing one circle in one revolution then the initial and final position will be the same.
2. Therefore the displacement in one complete revolution will be zero.

Step 3: Finding the average speed and average velocity:

Therefore,

$\mathrm{Average}\mathrm{speed}=\frac{\mathrm{Distance}}{\mathrm{Time}\mathrm{taken}}=\frac{\left(200\mathrm{\pi }\right)}{360}=\left(\frac{5\mathrm{\pi }}{9}\right){\mathrm{ms}}^{-1}$.

And, $\mathrm{Average}\mathrm{velocity}=\frac{\mathrm{Displacement}}{\mathrm{Time}\mathrm{taken}}=\frac{0}{360\mathrm{s}}=0$.

Hence, option (B) is the correct answer.