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.

​

Answer 1

Answer:

n 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

​  

Explanation: