Question

A body moves along a curved path of a quarter circle. what is the ratio of distance to displacem
ENT

Answer 1

Let the radius of the circle be r.

Distance traveled in quarter circle = $\frac{\pi \times r}{2}$

Displacement in a quarter circle = $\sqrt{r^2 +r^2}$ (using Pythagoras Theorem

Displacement = $r\sqrt{2}$

Ratio = $\frac{Distance}{Displacement}$

Ratio = $\frac{\pi \times r }{2\times r \sqrt{2} }$

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

Hence, the ratio between distance and displacement is $\frac{\pi }{2\sqrt{2} }$.