A body covered a distance of Lm along a curved path of a quarter circle.The ratio of distance to displacement.

\frac{π}{2 \sqrt{2}}

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\frac{2 \sqrt{2}}{π}

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\frac{π}{\sqrt{2}}

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\frac{\sqrt{2}}{π}

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Solution

The correct option is B $\frac{π}{2 \sqrt{2}}$
$\begin{matrix} T o t a l d i s t a n c e t r a v e l l e d = L f o r d i s p a c e m e n t \frac{π r}{2} = L S o, r = \frac{2 L}{π} d i s p l a c e m e n t = s h o r t e s t d i s t a n c e b e t w e e n i n i t i a l a n d f i n a l p o i n t s = r = \frac{2 \sqrt{2} L}{π} t h e r e f o r e, r a t i o = \frac{π}{2 \sqrt{2}} \end{matrix}$
Hence,
option $(A)$ is correct answer.

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Similar questions

A car travels $(\frac{1}{4})^{t h}$ of a circular path with radius r. Find the ratio of the distance to its displacement.

A) (- 3, 45^{\circ}), (7, 105^{\circ})

B) (\sqrt{2}, \frac{π}{4}), (2, \frac{π}{2})

C) (3, \frac{π}{6}), (7, \frac{π}{6})

(a, \frac{π}{2})

(3 a, \frac{π}{6})

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