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 and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed ω/2. The ring and disc are separated by frictionless ball bearings. The system is in the x-z plane. The point P on the inner disc is at a
distance R from the origin, where OP  makes an angle of 300 with the horizontal. Then with respect to the horizontal surface.

10112021388_k2.PNG


A) the point O has a linear velocity 3Rωi

B) the point P has a linear velocity 114Rωi34Rωk

C) the point P has a linear velocity 134Rωi34Rωk

D) the point P has a linear velocity (334)Rωi+14Rωk

Answer:

Option A,B

Explanation:

10112021566_k3.PNG

 Velocity of point O is 

  v0=(3Rω)ˆi

 VPO is R.ω2 in the direction shown in the figure. In vector form

 vPO=Rω2sin300ˆi+Rω2cos300ˆk=Rω4ˆi+3Rω4ˆi

 bu  vPO=vPvO

  vp=vpo+vo

 =(Rω4ˆi+3Rω4ˆk)+3Rωˆi

 =114Rωˆi+34Rωˆk