A sphere is rolling without slipping on a fix | vedclass

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(C) Let $\vec{V}_0$ be the velocity of the centre of the sphere. For a sphere rolling without slipping on a fixed horizontal surface:$\vec{V}_A = 0$ (

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$(A, C)$

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(C) Let $\vec{V}_0$ be the velocity of the centre of the sphere. For a sphere rolling without slipping on a fixed horizontal surface:$\vec{V}_A = 0$ (velocity of the point of contact)$\vec{V}_B = \vec{V}_0$ (velocity of the centre)$\vec{V}_C = 2\vec{V}_0$ (velocity of the topmost point)Now,let's evaluate the given options:For $(B)$: $\vec{V}_C - \vec{V}_B = 2\vec{V}_0 - \vec{V}_0 = \vec{V}_0$ and $\vec{V}_B - \vec{V}_A = \vec{V}_0 - 0 = \vec{V}_0$. Thus,$\vec{V}_C - \vec{V}_B = \vec{V}_B - \vec{V}_A$ is correct.For $(C)$: $|\vec{V}_C - \vec{V}_A| = |2\vec{V}_0 - 0| = 2|\vec{V}_0|$ and $2|\vec{V}_B - \vec{V}_C| = 2|\vec{V}_0 - 2\vec{V}_0| = 2|-\vec{V}_0| = 2|\vec{V}_0|$. Thus,$|\vec{V}_C - \vec{V}_A| = 2|\vec{V}_B - \vec{V}_C|$ is correct.Therefore,both $(B)$ and $(C)$ are correct statements.

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