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

A body covered a distance of 'z' metre along a semicircular path.

If it is a circular path then the distance covered by the body will be 2πr. But here, body covered a semi-circular path.

(Means, half of the circular path i.e. 2πr/2 = πr)

So, distance covered by body = πr

Let us assume that the radius of the semicircular path is (r).

Radius = Diameter/2

2 × Radius = Diameter

2r = Diameter

We have to find the magnitude of displacement of the body, and the ratio of distance to displacement.

Now, for a semicircular path displacement covered is equal to the diameter of semicircular path i.e. 2r.

Given in question that, the body covers a distance of (z) meter.

So, Distance is ''z' metre.

Now,

Distance is z and diameter is 2r which is equal to z.

i.e. 2r = z

r = z/2

So, Distance = πr = πz/2

And from above we have displacement = 2r

And 2r = z. So, Displacement = z

Therefore,

Distance/Displacement = (πz/2)/z = πz/2z = π/2

Answer 2

the body covers a distance of z meter along the semicircular path

We know that distance is the actual path travelled by the body between its initial and final position

the distance covered by the body

= perimeter of the semicircle

= π R

z = π R

R = Z / π

Displacement is the shortest distance travelled by the body between it's initial and final position

Displacement = diameter of the circle

Displacement = 2 R

Substituting R as Z / π

Displacement = 2 Z / π

Ratio of distance to Displacement

= z×π / 2 Z

= π /2

Ratio of distance to Displacement = π / 2