Question

An object is moving with uniform speed in a circle of radius r. Calculate the distance and displacement
(a) when it completes half the circle
(b) when it completes 3/4th of the circle.

Answer 1

The radius of the circle= $r$

(i) When it completes half circle:-

(Refer to Image 1)

Distance= $\frac{circumference}{2}=\frac{2\pi r}{2}$

Distance= $\pi r$

Displacement= $r+r=2r$

(ii) When it completes $3/4^{th}$ of the circle:-

The distance covered= $\frac{3}{4}\left(circumference\right)$

$\Rightarrow \frac{3}{4}\left(2\pi r\right)=\frac{3}{2}\pi r$

The displacement= $AB$ (Refer to Image 2)

By using pythagoras theorem

$A{B}^2=r^2+r^2$

$\Rightarrow A{B}^2=2r^2$

$\Rightarrow AB=\sqrt{2}r$

Displacement= $\sqrt{2}r$

Distance= $\frac{3}{2}\pi r$