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

displacement of the body is radius of the sc that is r

also we know circumference of the sc path is z = pie r = displacement

ratio is = pie r/ r

= pie

Answer 2

$\bf \dfrac{\pi }{2}$

Explanation :

Given :

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

If that is a circular path then the distance covered by the body must be 2πr. But, no here it is given that body covered a semi-circular path.

Therefore,

Half of the circular path -

$\implies \sf \dfrac{2\pi r}{2} = \pi r$

Hence, The body covered πr distance.

Consider the :

The radius of the semicircular path as -  r.

$\sf \dfrac{Diameter}{2} = Radius.\\ \\ \\\implies 2 \times Radius = Diameter\\ \\ \\\implies 2r = Diameter$

To Find :

The magnitude of displacement of the body, and the ratio of distance to displacement.

Solution :

Displacement = Diameter of semicircular path (2r)

It is given,

The body covers a distance of (z) meter.

So,

Distance = z

Therefore,

$\implies \sf 2r = z\\ \\ \\\implies r = \dfrac{z}{2}$

So,

Distance :

$\implies \sf 2r = z\\ \\ \\ \implies r = \dfrac{z}{2}$

According to this,

We have displacement = 2r

⇒ 2r = z.

⇒ Displacement = z

Now,

$\implies \dfrac{\bf Distance}{\bf Displacement}\\ \\ \\\implies \sf \dfrac{\pi z2}{z}\\ \\ \\\implies \sf \dfrac{\pi z}{2z}\\ \\ \\ \implies \sf \dfrac{\pi }{2}$