Question

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

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

Answer 1

The correct option is C

$\frac{\pi }{2\sqrt{2}}$

Distance travelled by the car = $\frac{1}{4}\times (\text{Circumference of the circle)}$ = $\frac{1}{4}\times 2\pi r$ = $\frac{\pi r}{2}$

Displacement is the shortest distance between two points which the body moves. In the diagram below, the displacement is shown by the letter x

As evident from the figure, $x^2$ = $r^2$ + $r^2$ = $2r^2$

Hence displacement, x = $\sqrt{2}$ r

Now, ratio of distace to displacement = $\frac{\frac{\pi r}{2}}{\sqrt{2}r}$ = $\frac{\pi }{2\sqrt{2}}$