Question

A body moving in a circle of radius ‘r’, covers ¾th of the circle. Find the
ratio of the distance to displacement

Answer 1

Solution :

⏭ Given:

✏ A body moving in a circle of radius 'r' , covers 3/4th of the circle.

⏭ To Find:

✏ The ratio of the distance to displacement.

⏭ Concept:

✏ Distance is defind as total length of path which is covered by body.

✏ Displacement is defind as the shortest distance between two points.

⏭ Calculation:

$\bigstar \: \boxed{ \large \sf \red{Distance}} \\ \\ \mapsto \sf \: Distance = \frac{3}{4} \times perimeter \\ \\ \mapsto \sf \: Distance= \frac{3}{4} \times 2\pi{r} \\ \\ \mapsto \sf \: \underline{ \blue{Distance = \frac{3}{2} \pi{r}}} \\ \\ \bigstar \: \boxed{ \large{ \green{ \sf{Displacement}}}} \\ \\ \mapsto \sf \: Displacement = \sqrt{ {r}^{2} + {r}^{2} } \\ \\ \mapsto \sf \: Displacement = \sqrt{2 {r}^{2} } \\ \\ \mapsto \sf \: \underline{ \pink{Displacement = \sqrt{2} r}} \\ \\ \bigstar \sf \: \frac{Distance}{Displacement} = \frac{3\pi \times \cancel{r}}{2 \sqrt{2} \times \cancel{r} } \\ \\ \orange{ \bigstar} \: \underline{ \boxed{ \bold{ \sf{ \purple{ \frac{Distance}{Displacement} = \frac{3\pi}{2 \sqrt{2}}}}}} } \: \orange{ \bigstar}$