A body covered a distance of 2 meture along a semicircular path. Calculate the magnitude of displacement of the body, and the ratio of distance to displace -ment ?
Answers
Answer:
Given:-
A body covered a distance of 'z' metre along a semicircular path.
To find:-
♠ The magnitude of displacement of the body.
♠ The ratio of distance to displacement.
Solution:-
The body covers a distance along a semi-circular path.
Distance is z and diameter is 2r which is equal to z.
i.e. 2r = z
or, r = z/2
Distance covered becomes half the perimeter of the circle = π/2
So, the distance covered by the path is 2π2/2 = πr = z
⇒ r = z/π
→ Displacement is the least length covered by the body.
(If the initial position was A, then distance = arc AB and displacement = AB, which is the diameter).
◘ So, displacement(S) = diameter of the circle (as a diameter of a circle into 2 equal semi-circles).
S = 2r = 2z/π
Now, ratio of the distance to the displacement = s/S
⇒s/S = z/(2z/π)
⇒s/S = π/2
⇒ s:S = π:2
Explanation:
