Question

A body moves along a curved path of a quarter of a circle. The ratio of distance to displacement is

• A. $\frac{\pi }{2\sqrt{2}}$
• B. $\frac{\sqrt{2}}{\pi }$
• C. $\frac{2\sqrt{2}}{\pi }$
• D. $\frac{\pi }{\sqrt{2}}$

Answer 1

The correct option is A $\frac{\pi }{2\sqrt{2}}$

Distance = Length of quarter circle path

$=\frac{2\pi r}{4}=\frac{\pi r}{2}$



From $△OAB$,

Displacement $=AB$

= $\sqrt{r^2+r^2}=\sqrt{2}r$

$\frac{\text{Distance}}{\text{displacement}}=\frac{\left(\frac{\pi r}{2}\right)}{\sqrt{2}r}$

$=\frac{\pi }{2\sqrt{2}}$

Final answer : (a)