Question

A body moves along the curved path of quarter circle . Calculate the ratio of distance to displacement
pls tell

Answer 1

Answer:

$\pi : 2\sqrt{2}$

Explanation:

Given,

A body moves along a curved path of quarter circle.

To Find :-

Ratio of Distance to Displacement.

Solution :-

Distance covered by body moving along a curved path of quarter circle = Perimeter of the quarter circle :-

Perimeter of the quarter circle = Perimeter of the circle/4

$=\dfrac{2\pi r}{4}$  

[ r = radius]

$=\dfrac{\pi r}{2}$

Displacement of the body moving along a curved path of quarter circle = Perimeter of the quarter circle :-

In the case of a quadrant, the term displacement indicates the hypotenuse side :-

$(hypotenuse\:side)^2=(opposite\:side)^2+(adjacent\:side)^2$

$(hypotenuse\:side)^2=r^2+r^2$

$(hypotenuse\:side)^2=2r^2$

hypotenuse side = displacement = √2r.

Ration of Distance to Displacement :-

$=\dfrac{\pi r}{2} : \sqrt{2}r$

$=\dfrac{\dfrac{\pi r}{2}}{\sqrt{2}r}$

$=\dfrac{\pi r}{2}\times \dfrac{1}{\sqrt{2}r}$

$=\pi : 2\sqrt{2}$