JEE Advanced2012PhysicsRotational MotionActual
The figure shows a system consisting of (i) a ring of outer radius 3 R rolling clockwise without slipping on a horizontal surface with angular speed and (ii) an inner disc of radius 2 R rotating anti-clockwise with angular speed / 2 . 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 O P makes an angle of 30^ with the horizontal. The
Options
- Athe point O has linear velocity 3 R i
- Bthe point P has linear velocity 11 4 R i + 3 4 R k .
- Cthe point P has linear velocity 13 4 R i - 3 4 R k
- Dthe point P has linear velocity (3- 3 4 ) R i + 1 4 R k
Correct answer
A. the point O has linear velocity 3 R i
Step-by-step solution
Velocity at centre 'O' v _ o =3 R i V _ P =3 R i - R 2 30^ i + R 2 30^ k V _ P = [3 R_ i - R_ 4 i ]+ 3 R_ 4 k or, V _ P = 11 4 R_ i + 3 4 R_ k