No, a larger stagger is needed. In a 400 m race, runners navigate two bends on a 400 m track but four bends on a 200 m track, requiring twice the total stagger distance.
In my school, the playground is too small to have a 400 m track, so the school constructed a 200 m track instead. Does this mean that we need a smaller stagger for the race tracks in my school (i.e., smaller than the stagger used in the Olympics), for the same 4 x 100 m relay race?
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No, the school track actually requires a larger stagger, not a smaller one.
On a running track, the stagger compensates only for the extra distance run around curved bends:
Extra distance per full lap = 2 x π x w, where w is lane width.
A 4 x 100 m relay covers 400 m in total:
On a standard 400 m track, a 400 m race is 1 complete lap, containing 2 curved bends (total angle 360°), requiring a stagger of 2πw.
On a 200 m track, a 400 m race requires 2 complete laps, which contains 4 curved bends (total angle 720°).
The extra distance run in an outer lane is 2 x (2πw) = 4πw.
Therefore, the total stagger needed on a 200 m track is twice as large as on a 400 m track.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 6 Measuring Space: Perimeter and Area Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-6/