Question

If the particle moves from A to B as shown in figure, then the ratio of displacement to distance covered by particle is (if R is the radius of track)

• A. $\frac{2\sqrt{2}}{3\pi }$
• B. $\frac{3\pi }{2\sqrt{2}}$
• C. $\frac{\pi }{\sqrt{2}}$
• D. $\frac{\pi }{2\sqrt{2}}$

Answer 1

The correct option is A $\frac{2\sqrt{2}}{3\pi }$

Distance =APB=$2\pi r\times \frac{3}{4}=\frac{3\pi R}{2}$

Displacement =AB=$R\sqrt{2}$

$\frac{Displacement}{Distance}=\frac{R\sqrt{2}}{3\pi R}\times 2=\frac{2\sqrt{2}}{3\pi }$