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 and displacement

Answer 1

Given :

• x = (2π r/2) or r = x/π
• diameter = 2 r = 2 x/π

To find :

• magnitude of displacement of the body
• the ratio of distance and displacement

Solution :

magnitude of displacement = diameter

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 2 x/π

distance/displacement = x/(2x/π)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = π/2

=> magnitude of displacement of the body is 2 x/π

the ratio of distance and displacement 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