Correct option is B
Given:
Five adjacent semi-circular tracks.
Each track has mean length = 100 meters.
Width of each track = 2.5 meters.
Inner track subtends an angle = 1.00 rad.
Solution:
Now Step-by-step:
Step 1: Find the mean radius of the inner track.
Mean length = Angle × Mean radius
=> 100 = 1.00 × r
=> r = 100 meters
So, mean radius of inner track = 100 meters.
Step 2: Find the mean radius of the outermost track.
Total number of tracks = 5
Each track has width = 2.5 m
So, the outermost track is 4 widths away from the inner track.
Thus,
Extra radius = 4 × 2.5 = 10 meters
Mean radius of outermost track = 100 + 10 = 110 meters.
Step 3: Now find angle subtended by the outermost track.
Again use:
Mean length = Angle × Mean radius
Thus,
100 = Angle × 110
Angle = 100/110
Angle = 0.909 rad
Now 0.909 is approximately 0.91 rad.
Therefore, Option (b) 0.91 rad is the correct answer.
Short Trick:
When radius increases and arc length is fixed,
New Angle = (Old Radius / New Radius) × Old Angle
Here:
New Angle = (100/110) × 1.00 = 0.909 ≈ 0.91 rad.
