Which of the following statements is incorrect for a spherical body rolling without slipping on a rough horizontal ground at rest?

  • A
    The acceleration of a point in contact with the ground is zero.
  • B
    The acceleration of $C.O.M.$ of the sphere may or may not be zero.
  • C
    Friction force may or may not be zero.
  • D
    Work done by friction with respect to the ground on the body is zero.

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$A$ sphere is rolling without slipping on a fixed horizontal plane surface. In the figure,$A$ is the point of contact,$B$ is the centre of the sphere and $C$ is its topmost point. Then,
$(A)$ $\vec{V}_C-\vec{V}_A=2(\vec{V}_B-\vec{V}_C)$
$(B)$ $\vec{V}_C-\vec{V}_B=\vec{V}_B-\vec{V}_A$
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$(D)$ $|\vec{V}_C-\vec{V}_A|=4|\vec{V}_B|$

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Find the displacement of the point of contact with the ground when a ring of radius $R$ completes a half-rotation.

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