In a circular car race tracks, one has to maintain a speed proportional to the square - root of radius of the track to avoid accident. There are concentric circular tracks with radii 12.25 m, 49 m, 110.25 m and 196 m respectively. If the average speed of a racer who covers all four tracks is 75.6 km/hr, what is the speed with he covered the third track (in m/s)? Neglect the time taken to shift between two tracks.

In a circular car race tracks, one has to maintain a speed proportional to the square - root of radius of the track to avoid accident. There are concentric circular tracks with radii 12.25 m, 49 m, 110.25 m and 196 m respectively. If the average speed of a racer who covers all four tracks is 75.6 km/hr, what is the speed with he covered the third track (in m/s)? Neglect the time taken to shift between two tracks. Correct Answer 33

Given that v ∝ r^0.5

Let v/r^0.5 = k

For first track, r = 12.25

∴ v = 3.5 k

Time taken = Distance travelled/Time taken

= 2 π r/v

= 2 × 22/7 × 12.25/3.5 k = 22/k

For second track, r = 49

∴ v = 7 k

Time taken = Distance travelled/Time taken

= 2πr/v = 44/k

For third track, r = 110.25

∴ v = 10.5 k

Time taken = Distance travelled/Time taken

= 2πr/v = 66/k

For fourth track, r = 196

∴ v = 14 k

Time taken = Distance travelled/Time taken

= 2πr/v = 88/k

Total time taken = 22/k + 44/k + 66/k + 88/k = 220/k

Total distance covered = 2 π (12.25 + 49 + 110.25 + 196) = 2310 m

Average speed = 2310/220/k = 10.5 k m/s

Given that the average speed = 75.6 km/hr = 21 m/s

10.5 k = 21

∴ k = 2