A body covered a distance of 5 m along a semicircular path. The ratio of distance to displacement is
Question
A body covered a distance of 5 m along a semicircular path. The ratio of distance to displacement is
Solution
The distance covered by the body is 5 m along a semicircular path.
The displacement of the body is the straight line distance from the initial to the final position. In a semicircular path, the displacement is equal to the diameter of the semicircle.
The diameter of a semicircle is twice the radius. We know that the circumference of a full circle is 2πr. Therefore, the length of a semicircle is πr. If this length is 5 m, then the radius r is 5/π.
Therefore, the diameter (which is the displacement in this case) is 2r = 2*(5/π) = 10/π.
The ratio of distance to displacement is therefore 5/(10/π) = π/2.
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