Question

A particle moves from A to B in a circular path of radius R covering an angle e as shown in figure. Find the
ratio of distance and magnitude of displacement of the particle.
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Answer 1

Answer:

correct answer = θ/2sinθ/2

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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

​