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Q.

A small particle of mass m is given an initial high velocity in the horizontal plane and winds its cord around the fixed vertical shaft of radius a. All motion occurs essentially in horizontal plane. If the angular velocity of the cord is ω0, when the distance from the particle to the tangency point is r0, then the angular velocity of the cord ω after it has turned through an angle θ is :

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a

ω= ω0

b

ω=ar0 ω0

c

ω=ω01-ar0θ

d

ω= ω0θ

answer is C.

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Detailed Solution

r=r0-aθ

In the process v remains constant, so 

 ω0 r0=ωr ω= ω0 r0r0-aθ=ω01-aθr

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A small particle of mass m is given an initial high velocity in the horizontal plane and winds its cord around the fixed vertical shaft of radius a. All motion occurs essentially in horizontal plane. If the angular velocity of the cord is ω0, when the distance from the particle to the tangency point is r0, then the angular velocity of the cord ω after it has turned through an angle θ is :