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

  $\overrightarrow{\mathbf{v}}_C-\overrightarrow{\mathbf{v}}_A=2\left(\overrightarrow{\mathbf{v}}_B-\overrightarrow{\mathbf{v}}_C\right)$
• Correct answer
  B

  $\overrightarrow{\mathbf{v}}_C-\overrightarrow{\mathbf{v}}_B=\overrightarrow{\mathbf{v}}_B-\overrightarrow{\mathbf{v}}_A$
• Correct answer
  C

  $\left|\overrightarrow{\mathbf{v}}_C-\overrightarrow{\mathbf{v}}_A\right|=2\left|\overrightarrow{\mathbf{v}}_B-\overrightarrow{\mathbf{v}}_C\right|$
• D

  $\left|\overrightarrow{\mathbf{v}}_C-\overrightarrow{\mathbf{v}}_A\right|=4\left|\overrightarrow{\mathbf{v}}_B\right|$

Solution

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

Hence, the correct answer is options: 'B', 'C'.