Question

A particle moves from A to B in a circular path of radius R covering an angle 0 as shown in figure. Find the
ratio of distance and magnitude of displacement of the particle







​

Answer 1

Answer:

In triangle ABO, ∠AOB=θ

AB is the displacement of the particle.

Using cosθ=

2(AO)(BO)

AO

2

+BO

2

−AB

2

Or cosθ=

2R

2

R

2

+R

2

−AB

2

We get AB

2

=2R

2

−2R

2

cosθ

Or AB

2

=2R

2

(1−cosθ)=2R

2

×2sin

2

(

2

θ

)

⟹ AB=2Rsin

2

θ

Distance covered by the particle d=Rθ

Thus ratio of distance and displacement

AB

d

=

2sin

2

θ

θ

Answer 2

Please refer to the Attachment.....

Hope it was helpful for you ☺️☺️