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IIT JEE Advanced 2012 Paper 2

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Question : 18

Total: 60

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 ω/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 OP makes an angle of 30° with the horizontal. Then, with respect to the horizontal surface,

the point O has linear velocity 3Rω
^
i
.
the point P has linear velocity
11
4
Rω
^
i
+
√3
4
Rω
^
k
.
the point P has linear velocity
13
4
Rω
^
i
−
√3
4
Rω
^
k
the point P has linear velocity (3−
√3
4
)Rω
^
i
+
1
4
Rω
^
k
.

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