Question

An object covers 1/4 of the circular path, what will be the ratio of the distance and displacement of the object?

Answer 1

distance traveled $=\frac{2\pi r}{4}=\frac{\pi r}{2}$
displacement $=AB=\sqrt{r^2+r^2}=r\sqrt{2}$
$\frac{\text{distance}}{\text{displacement}}=\frac{\frac{\pi r}{2}}{\sqrt{2}r}$
$ratio=\frac{\pi }{2\sqrt{2}}$