A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, $A$ is the point of…

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,

1. $\overrightarrow{\mathbf{v}}_C-\overrightarrow{\mathbf{v}}_A=2\left(\overrightarrow{\mathbf{v}}_B-\overrightarrow{\mathbf{v}}_C\right)$
2. $\overrightarrow{\mathbf{v}}_C-\overrightarrow{\mathbf{v}}_B=\overrightarrow{\mathbf{v}}_B-\overrightarrow{\mathbf{v}}_A$
3. $\left|\overrightarrow{\mathbf{v}}_C-\overrightarrow{\mathbf{v}}_A\right|=2\left|\overrightarrow{\mathbf{v}}_B-\overrightarrow{\mathbf{v}}_C\right|$
4. $\left|\overrightarrow{\mathbf{v}}_C-\overrightarrow{\mathbf{v}}_A\right|=4\left|\overrightarrow{\mathbf{v}}_B\right|$

Solution

$ v_A=0, v_B=v \text { and } v_C=2 v $

Asked in: JEE Advanced 2009 (Paper 2)

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