Question

A body covered a distance of x metre along a semicircular path. Calculate the magnitude of displacement of the body, and the ratio of distance to displacement.

Answer 1

Total distance covered is half the circumference of circular path.

So, distance d = (2πr)/2 = πr
We have been given that
d = x
So, πr = x
So, r = x/π



Now, the displacement is the shortest path between initial point and final point.

Here, displacement s = diameter = 2r
Therefore, s=2x/π

Also, ratio is d/s = (πr)/2r = π/2

Thus,
Magnitude of displacement is 2x/π

And, ratio of distance to displacement is π/2

Answer 2

Answer:

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Explanation:

Total distance covered is half the circumference of circular path.

So, distance d = (2πr)/2 = πr

We have been given that

d = x

So, πr = x

So, r = x/π

Now, the displacement is the shortest path between initial point and final point.

Here, displacement s = diameter = 2r

Therefore, s=2x/π

Also, ratio is d/s = (πr)/2r = π/2

Thus,

Magnitude of displacement is 2x/π

And, ratio of distance to displacement is π/2