Answer: Option B
:
B
Given:
Diameter of the circle, $d=400m$
Time taken to complete one circle, $T=40s$
Total time of motion, $T_2=2min20s$
Circumference of circle, $C=\pi d$
Speed is defined as the ratio of distance covered to time taken.
Hence, speed of the runner
$v=\frac{C}{T}=\frac{\pi d}{T}$
Total time of motion, $T_2=2min20s=140s$
Total distance covered is given by:
$D=v{T}_2$
$D=\pi d\frac{T_2}{T}$
$D=\pi \times 400\times \frac{140}{40}$
$D\approx 4400m$
No. of rounds completed:
$n=\frac{\text{Total distance covered}}{\text{Circumference of the circle}}$
$n=\frac{D}{\pi d}$
$n=\frac{T_2}{T}$
$n=\frac{1400}{40}=3.5$
This means that he will be at the diametrically opposite end, i.e., he starts at A and ends at B.
Hence displacement, $s=2r=400m$