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IIT JEE Advanced 2012 Paper 2
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© examsnet.com
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,
[JEE Adv 2012 P2]
the point O has linear velocity
3
R
ω
^
i
.
the point P has linear velocity
11
4
R
ω
^
i
+
√
3
4
R
ω
^
k
.
the point P has linear velocity
13
4
R
ω
^
i
−
√
3
4
R
ω
^
k
the point P has linear velocity
(
3
−
√
3
4
)
R
ω
^
i
+
1
4
R
ω
^
k
.
Validate
Solution:
We have
→
v
O
=
(
3
R
)
ω
^
i
= 0 ⇒
→
v
O
=
3
R
ω
^
i
Therefore,
→
V
P
,
O
=
−
R
ω
4
^
i
+
R
ω
√
3
4
^
k
and
→
v
p
=
→
v
P
,
O
+
→
v
O
=
11
4
R
ω
^
i
+
R
ω
√
3
4
^
k
© examsnet.com
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