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Rotational Motion question

2012 · Shift 2 · Q48
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Rotational Motion question

2012 · Shift 2 · Q48

JEE AdvancedPhysicsRotational MotionMultiple correct+4 / −1
The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed ω\omegaω and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed ω2{\omega \over 2}2ω​. The ring and disc are separated by frictionless ball bearings. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 30∘30^\circ30∘ with the horizontal. Then with respect to the horizontal surface, IIT-JEE 2012 Paper 2 Offline Physics - Rotational Motion Question 58 English
  1. A
    the point O has linear velocity 3Rωi^3R\omega \widehat i3Rωi
  2. B
    the point P has linear velocity 114Rωi^+34Rωk^{{11} \over 4}R\omega \widehat i + {{\sqrt 3 } \over 4}R\omega \widehat k411​Rωi+43​​Rωk
  3. C
    the point P has linear velocity 134Rωi^−34Rωk^{{13} \over 4}R\omega \widehat i - {{\sqrt 3 } \over 4}R\omega \widehat k413​Rωi−43​​Rωk
  4. D
    the point P has linear velocity (3−34)Rωi^+14Rωk^\left( {3 - {{\sqrt 3 } \over 4}} \right)R\omega \widehat i + {1 \over 4}R\omega \widehat k(3−43​​)Rωi+41​Rωk
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