Question

A body coverd a distance of 'z' metre along a semi circular path. Calculate the magnitude of dosplacement of the body and the ratio of distance to displacement.

Answer 1

Answer:

Distance is z and diameter is 2r which is equal to z. Now, Distance/Displacement = (πz/2)/z = πz/2z = π/2 [ Answer. ]

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Answer 2

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).

\huge \boxed{S =2r=2z/\pi }

S=2r=2z/π

Now, ratio of the distance to the displacement = s/S

⇒s/S = z/(2z/π)

⇒s/S = π/2

\huge\boxed{\implies s:S = \pi :2}

⟹s:S=π:2