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Question

If the ring performs combined rotational and translational motion on a frictionless horizontal surface as shown in figure, find the magnitude of the velocity at a point P on the ring.


A
219 m/s
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B
38 m/s
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C
29 m/s
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D
19 m/s
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Solution

The correct option is D 19 m/s
Radius, R=1 m
Magnitude of velocity of COM of the ring,
|VO|=V0=5 m/s
But, VP=VO+VPO
Magnitude of velocity of point P w.r.t centre of ring (O)
|VPO|=Rω=1×2=2 m/s
120 is the angle between VO and VPO as shown in figure:


Magnitude of velocity of point P is,
VP=|VO|2+|VPO|2+2 (|VO|) (|VPO|)×cos120
where cos120=12
VP=(5)2+(2)2+2×5×2×(12)

VP=25+410=19 m/s

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