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Question

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 anticlockwise with angular speed ω2. The ring and the disc are separated by frictionless ball bearings. The system is in the xz-plane. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 30 with this horizontal, where O is the centre of the disc. Then with respect to this horizontal surface

A
The point O has linear velocity 3Rω^i
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B
The point P has linear velocity (114Rω ^i+34Rω ^k)
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C
The point P has linear velocity (134Rω ^i34Rω ^k)
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D
The point P has linear velocity ((334)R ω ^i+14Rω ^k)
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Solution

The correct option is B The point P has linear velocity (114Rω ^i+34Rω ^k)

V0(3R)ω ^i=0.
V0=3R ω ^i.
Now, VP,O=Rω4^i+Rω34^j
Vp=VP,O+V0
=Rω4^i+Rω34^j+3Rω^i
=114Rω^i+Rω34^j.
Hence, the correct options are (a) and (b).

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