Question

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

Answer 1

Answer:

In triangle ABO,   ∠AOB=θ

AB is the displacement of the particle.

Using    cosθ=2(AO)(BO)AO2+BO2−AB2

Or    cosθ=2R2R2+R2−AB2

We get   AB2=2R2−2R2cosθ

Or    AB2=2R2(1−cosθ)=2R2×2sin2(2θ)

⟹ AB=2Rsin2θ

Distance covered by the particle  d=Rθ

Thus ratio of distance and displacement   ABd=2sin2θθ