Question

A body covered a distance of X meters along a semi-circular path. calculate the magnitude of displacement of the body and the ratio of distance to displacement.

Answer 1

Step 1: Given data

The distance covered on the semi-circular path is X meters.

Step 2: Finding the displacement of the body

Let r be the radius of the semicircular path

Since X is the distance along the semi-circular path,

So we can write

$\pi r=X$

$Or,r=\frac{X}{\pi }$

Now,

Displacement of the body = Distance between the initial and final position

= Diameter of the circular path

Or, Displacement = $2r=\frac{2X}{\pi }$

Now,

The ratio of distance to displacement = $\frac{X}{\frac{2X}{\pi }}$

After solving

Ratio = $\pi :2$
Hence the ratio between the distance and displacement is $\pi :2$