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Q.

A hoop rolls on a horizontal ground without slipping with linear speed v. Speed of a particle P on the circumference of the hoop at angle θ is:

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a

2v sin (θ2)

b

v sin θ

c

2v cos (θ2)

d

v cos θ

answer is A.

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Detailed Solution

vp = v2+v2+2vv cos (180-θ)⇒vp  = 2v2[1-cos θ]           = 2v sin (θ2)
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A hoop rolls on a horizontal ground without slipping with linear speed v. Speed of a particle P on the circumference of the hoop at angle θ is: