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/sRadius, 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+4−10=√19 m/s

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