Question

A particle moves around a circle with radius r and it completes ¼ of the whole circle. Find the ratio between the distance and displacement.​

Answer 1

Answer:

4 ratio 5

Step-by-step explanation:

hope it helps you

Answer 2

Answer:

Radius of the circle = r

distance covered by the the particle = 1/4 X circumference

1/4 X2$\pi$r

1/2 X $\pi$r

distance = $\pi$r/2

Let the particle moves from A to B

the shortest distance is the chord AB

from triangle AOB,

$AB^{2}$ = $AO^{2}$ + $BO^{2}$

$AB^{2}$ =  $r^{2}$ + $r^{2}$

$AB^{2}$ =2$r^{2}$

AB =$\sqrt{2}$r

Displacement =$\sqrt{2}$r

Now,

distance : displacement

$\pi$r/2  : $\sqrt{2}$r

$\pi$     : 2$\sqrt{2}$

22/7 : 2$\sqrt{2}$

11/7 : $\sqrt{2}$

or

11 : 7$\sqrt{2}$