Question

An athlete completes one round of a circular track of radius $R$ in $40$ sec. What will be the magnitude of displacement at the end of $2$ min $20$ sec?

• A. Zero
• B. $2R$
• C. $2\pi R$
• D. $7\pi R$

Answer 1

Answer: (B)

Step 1: Given that:

The radius of the circular track = $R$

Time(t) to complete one round of circular track by athlete = $40sec$

Total given time(T) = $2min20sec$ = $2\times 60sec+20sec=140sec$

Step 2: Calculation of the magnitude of displacement :

Displacement = Shortest distance between the initial and final point of the path

In the circular path, for one complete round, the initial and final point is the same.

Hence,

Displacement in one complete round of circular track = $0$

Number of complete turns(n) in the given time = $\frac{Totaltime}{timetakentocompleteoneround}$

Therefore; $n=\frac{140sec}{40sec}=3.5$

In half round the shortest path = diameter of the circular path

Thus, the total displacement of the athlete = Total displacement in three complete rounds + displacement in 0.5 round

= 0 + diameter of the circular track
= $2R$

Thus,

Option C) $2R$ is the correct option.