Question

. A body covered a distance of z metre along a semicircular path. Calculate the magnitude of displacement of the body, and the ratio of distance to displacement?

Answer 1

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).

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

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

⇒s/S = z/(2z/π)

⇒s/S = π/2

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

Answer 2

Explanation:

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