One
morning while I was jogging around my apartment complex, I got a
doubt. Let us suppose that I am jogging in a circular path and
another person is also jogging in a parallel circular path (with a
different radius). What is the difference between the distances
travelled by me and the other person? Even if the difference between
the radii is small, the difference between total distances travelled
is more. why so? what is the underlying concept here?

Let
us consider that person ‘A’ is jogging in outer circle of radius
‘R’ and ‘B’ is jogging in an inner circle of radius ‘r’.
Obviously R > r. The distance travelled by A in one round is
nothing but the length of circumference of the circular path he
travelled.

The distance travelled by A = 2πR

Similarly,
the distance travelled by B = 2πr

Difference
of the distances = 2π(R-r).

The
difference of distances travelled in one round is multiplied by a
factor ‘2π’ to the difference of radii of the two circular
paths. If we consider the approximate value of ‘π’ as 3.14, the
multiplying factor becomes ‘6.28’. This means, if B is jogging at
2 ft lesser radial length to that of A, the total distance travelled
by B in one round is around 12 ft less than that of A. This is only
for one round. If we consider for 10 rounds, the difference becomes
120 ft.

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