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

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1. Answer:

   [tex]\pi : 2\sqrt{2}[/tex]

   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

   [tex]=\dfrac{2\pi r}{4}[/tex]

   [ r = radius]

   [tex]=\dfrac{\pi r}{2}[/tex]

   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 :-

   [tex](hypotenuse\:side)^2=(opposite\:side)^2+(adjacent\:side)^2[/tex]

   [tex](hypotenuse\:side)^2=r^2+r^2[/tex]

   [tex](hypotenuse\:side)^2=2r^2[/tex]

   hypotenuse side = displacement = √2r.

   Ration of Distance to Displacement :-

   [tex]=\dfrac{\pi r}{2} : \sqrt{2}r[/tex]

   [tex]=\dfrac{\dfrac{\pi r}{2}}{\sqrt{2}r}[/tex]

   [tex]=\dfrac{\pi r}{2}\times \dfrac{1}{\sqrt{2}r}[/tex]

   [tex]=\pi : 2\sqrt{2}[/tex]

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