The figure shows four tracks (either half - or quarter circles) that can be take

Question

The figure shows four tracks (either half - or quarter circles) that can be taken by a train, which moves at a constant speed. Rank the tracks according to the magnitude of a train's acceleration on the curved portion, greatest first. If multiple tracks rank equally, use the same rank for each, then exclude the intermediate ranking (i.e. if objects A, B, and C must be ranked, and A and B must both be ranked first, the ranking would be A: 1, B: 1, C: 3). If all tracks rank equally, rank each as "1". Track 1 Track 2 Track 3 Track 4 Greatest Second Greatest

Explanation / Answer

Radius of track 3 > radius of track 4 > radius of track 1 > radius of track 2

Thus

r3 > r4 > r1 > r2

We use centripetal force equation as below,

F= mv^2/r

Acceleration a=F/m = v^2/r

Thus ‘a’ is inversely proportional to radius of track r. As ‘r’ increases ‘a’ decreases and as ‘r’ decreases ‘a’ increases.

Hence

a3 < a4 < a1 < a2

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