An object moving in a circular path and covered $\frac{3}{4}\mathrm{th}$  distance on the perimeter of the path to reach from A and B. If ‘r’ is radius of the circular path, then the ratio between distance travelled and displacement by the object between A and B is

The distance travelled by the object in a circular path is $=\mathrm{angle}\times \mathrm{radius}$

After completion of $\frac{3}{4}\mathrm{th}$ the circle turned angle by radius vector  = 270°
$\begin{array}{l}{180}^{\circ }\to \mathrm{\pi }\\ {270}^{\circ }\to ?\\ \frac{180}{270}=\frac{\mathrm{\pi }}{\mathrm{x}}\\ \mathrm{x}=\frac{\mathrm{\pi }\times 270}{180}=\frac{3\mathrm{\pi }}{2}\end{array}$
Distance (s) $=\frac{3\mathrm{\pi }}{2}\mathrm{r}$
Displacement $=\sqrt{2}\mathrm{r}$

$\frac{\text{distance}}{\mathrm{displacement}}=\frac{\frac{3\mathrm{\pi }}{2}\mathrm{r}}{\sqrt{2}\mathrm{r}}=\frac{3\mathrm{\pi }}{2\sqrt{2}}$