A sphere is rolling without slipping on a fixed horizontal plane … - Vidyadip

MCQ

A sphere is rolling without slipping on a fixed horizontal plane surface. $A$ is the point of contact, $B$ is the centre of the sphere and $C$ is top most point.Then

A
${\vec v_C}\,\, - \,\,{\vec v_A}\,\, = \,2({\vec v_B}\,\, - \,\,{\vec v_C}\,)\,$
✓
${\vec v_C}\,\, - \,\,{\vec v_B}\,\, = \,{\vec v_B}\,\, - \,\,{\vec v_A}\,$
C
$|{\vec v_C}\,\, - \,\,{\vec v_A}|\,\, = \,2({\vec v_B}\,\, - \,\,{\vec v_C}\,)\,$
D
$|{\vec v_C}\,\, - \,\,{\vec v_A}|\,\, = \,4|{\vec v_B}|\,$

✓

Answer

Correct option: B.

${\vec v_C}\,\, - \,\,{\vec v_B}\,\, = \,{\vec v_B}\,\, - \,\,{\vec v_A}\,$

b
If $\vec{V}_{0}$ is the velocity of centre of the sphere, then

$\vec{V}_{C}=2 \vec{V}_{0}, -\vec B=\vec{V}_{0}$ and$-\vec A=0$

$\therefore \vec{V}_{\mathcal{C}}-\vec{V}_{B}=2 \vec{V}_{0}-\vec{V}_{0}=\vec{V}_{0}$

$\vec{V}_{B}-\vec{V}_{A}=\vec{V}_{0}-\overrightarrow{0}=\vec{V}_{0}$

$\therefore \vec{V}_{C}-\vec{V}_{B}=\vec{V}_{B}-\vec{V}_{A}$

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