a body covers a distance of X metre along a semicircular path. calculate the magnitude of displacement of body, and the ratio of distance to displacement?
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distance is the actual path covered by the body
distance =π R
Displacement is the shortest distance between the initial and final position
Displacement =2 R
Ratio of distance to Displacement
dist/displacement
=π R /2R
=π/2
distance /displacement = π/2
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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
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