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Question

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. Motion occurs essentially in horizontal plane (assume gravity free space). The angular velocity of the cord is ω0 when the distance from the particle to the tangency point is r0.


  1. The angular velocity of the cord after it has turned through an angle is

  2. The angular velocity of the cord after it has turned through an angle  is 

  3. The KE of the particle will increase

  4. The KE of the particle will remain same


Solution

The correct options are
A

The angular velocity of the cord after it has turned through an angle is


D

The KE of the particle will remain same


Speed v will remain same, as T is perpendicular to v always. Hence KE remains same.

v=ω0r0=ω(r0aθ)

ω=ω0r0r0aθ=ω01aθr0

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