Question

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

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

Answer 1

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

Total circular distance, $2\pi r$

Quarter circular distance,$D=$ $\frac{2\pi r}{4}=\frac{\pi r}{2}$

Displacement, $s=r\sqrt{2}$

Ratio = $\frac{D}{s}=\frac{\pi r/2}{r\sqrt{2}}=\frac{\pi }{2\sqrt{2}}$

Hence, ratio is $\frac{\pi }{2\sqrt{2}}$