Question

An athlete completes one round of circular track of radius r in 30 s with uniform speed. The ratio of distance to the displacement traveled by the athlete at the end of 45 s is

• A. $2r$
• B. $\frac{2r}{3}$
• C. $\frac{3\pi }{2}$
• D. $3\pi$

Answer 1

The correct option is C

$\frac{3\mathrm{\pi }}{2}$

Step 1: Given Data

1. The radius of the circular path is r.
2. Time taken by the athlete to complete one complete circle is 30 seconds.

Step 2: Calculating the ratio of distance to displacement

1. The distance covered by the athlete in 30 s will be equal to the circumference of the circular path ( $2\mathrm{\pi r}$)
2. So the distance covered by the athlete in 45 s will be $\frac{2\mathrm{\pi r}}{30}\times 45$ = $3\mathrm{\pi r}$
3. So we can say that the athlete will move a complete and a half-circle of the path in 45 s.
4. Now the displacement of the athlete in 45 s will be equal to the diameter of the circular path that is equal to$2r$.
5. The ratio of distance to the displacement of the athlete at the end of 45 s is $\frac{dis\tan ce}{displacement}$= $\frac{3\mathrm{\pi r}}{2r}$ = $\frac{3\mathrm{\pi }}{2}$

Hence,

The ratio of distance to the displacement of the athlete at the end of 45 s is$\frac{3\mathrm{\pi }}{2}$.