question_answer

A body covered a distance of L m along a curved path of a quarter circle. The ratio of distance to displacements

A) \[\frac{\pi }{2\sqrt{2}}\]

B) \[\frac{2\sqrt{2}}{\pi }\]

C) \[\frac{\pi }{\sqrt{2}}\]          

D) \[\frac{\sqrt{2}}{\pi }\]

Correct Answer: A

Solution :

[a] Displacement \[{{d}_{1}}=\sqrt{2}r\] Distance from A to B \[{{d}_{2}}=\left( \frac{\pi r}{2} \right)\] \[\frac{{{d}_{2}}}{{{d}_{1}}}=\frac{\frac{\pi r}{2}}{\sqrt{2}r}=\left( \frac{\pi }{2\sqrt{2}} \right)\]