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:
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:
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