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Question

According to question,

Let $\vec{\omega}$ be the angular velocity of the sphere. Let $A B=\vec{r}$ and hence $A C=2 \vec{r}$

The velocities $\ve

Vedclass · Accepted Answer

$|{\overline V _A} - {\overline V _A}| = 2\,\,|{\overline V _B} - {\overline V _C}|$

Vedclass · Answer

According to question,

Let $\vec{\omega}$ be the angular velocity of the sphere. Let $A B=\vec{r}$ and hence $A C=2 \vec{r}$

The velocities $\vec{v}_B$ and $\vec{v}_C$ are related to $\vec{v}_A$ by

$	herefore \vec{V}_B =\vec{V}_A+\vec{\omega} 	imes \vec{r}$

$\vec{V}_C =\vec{V}_A+\vec{\omega} 	imes(\overrightarrow{2 \vec{r}})$

$	herefore \vec{v}_C=\vec{v}_A+2 \vec{\omega} 	imes \vec{r}$

$\vec{V}_C-\vec{V}_A=2 \vec{\omega} 	imes \vec{r}$

$	herefore \quad \vec{V}_C-\vec{V}_A=-2(2)$

and $\vec{V}_C-\vec{V}_B=\vec{\omega} 	imes \vec{r}$

$\vec{V}_C-\vec{V}_B={\overrightarrow{V_B}}-\vec{V}_A \quad(4)$

Also, since sphere is rolling without slipping,

$	herefore \overrightarrow{V_A}=\overrightarrow{0} 	ext {. }$

Therefore, from $(3)$,

$\left|\overrightarrow{V_C}-\vec{V}_Aight|=2\left|\vec{V}_B-\vec{V}_Cight|$

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