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Wheel in pure rolling: speed of a rim point level with the centre

The same question, asked 2 times: 2021 Paper 13*, 4 Apr 2025. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 13

    3
    A wheel is undergoing pure rolling on a horizontal surface as shown. The point on rim of wheel at a same horizontal level as center has velocity xV0\sqrt{x}V_{0}. The xx is

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  2. Question 2

    4 Apr 2025

    87
    A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is 8 m/s8\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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