A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is 8 m/s. The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be: (a) 4√(2) m/s (b) 8 m/s (c) 4 m/s (d) 8√(2) m/s

Answer: (a). For rolling, top point speed = 2vcm = 8 ⇒ vcm = 4 m/s. A rim point level with the centre has velocity vcm (forward) and Rω = vcm (vertical), at right angles. Speed = √(2) vcm = 4√(2) m/s. So the answer is (a).

A wheel is rolling on a plane surface. The speed of a particle on the… | JEE Main 2025 (4 Apr, Shift 2)

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Rolling Motion

A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is $8\text{ m/s}$ . The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be:

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Answer: (a)

For rolling, top point speed $= 2v_{cm} = 8 \Rightarrow v_{cm} = 4$ m/s.
A rim point level with the centre has velocity $v_{cm}$ (forward) and $R\omega = v_{cm}$ (vertical), at right angles.
Speed $= \sqrt{2}\,v_{cm} = 4\sqrt{2}$ m/s.
So the answer is (a).

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