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(B) Let the velocity of the centre of mass $B$ be $\vec{V}_B = V\hat{i}$.For pure rolling,the velocity of the point of contact $A$ is $\vec{V}_A = 0$.

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$(ii), (iii)$

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(B) Let the velocity of the centre of mass $B$ be $\vec{V}_B = V\hat{i}$.For pure rolling,the velocity of the point of contact $A$ is $\vec{V}_A = 0$.The velocity of the topmost point $C$ is $\vec{V}_C = \vec{V}_B + \vec{\omega} 	imes \vec{r}_{BC} = V\hat{i} + V\hat{i} = 2V\hat{i}$.Checking the statements:$(i) \vec{V}_C - \vec{V}_A = 2V\hat{i} - 0 = 2V\hat{i}$.$2(\vec{V}_B - \vec{V}_C) = 2(V\hat{i} - 2V\hat{i}) = -2V\hat{i}$.Since $2V\hat{i} 
eq -2V\hat{i}$,statement $(i)$ is incorrect.$(ii) \vec{V}_C - \vec{V}_B = 2V\hat{i} - V\hat{i} = V\hat{i}$.$\vec{V}_B - \vec{V}_A = V\hat{i} - 0 = V\hat{i}$.Since $V\hat{i} = V\hat{i}$,statement $(ii)$ is correct.$(iii) |\vec{V}_C - \vec{V}_A| = |2V\hat{i} - 0| = 2V$.$2|\vec{V}_B - \vec{V}_C| = 2|V\hat{i} - 2V\hat{i}| = 2|-V\hat{i}| = 2V$.Since $2V = 2V$,statement $(iii)$ is correct.$(iv) |\vec{V}_C - \vec{V}_A| = 2V$.$4|\vec{V}_B| = 4V$.Since $2V 
eq 4V$,statement $(iv)$ is incorrect.Thus,statements $(ii)$ and $(iii)$ are correct.

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