A) Velocity and acceleration both are perpendicular to r \[\vec{r}.\]
B) Velocity and acceleration both are parallel to \[\vec{r}.\]
C) Velocity is perpendicular to \[\vec{r}.\]and acceleration is directed towards the origin
D) Velocity is perpendicular to \[\vec{r}.\]and acceleration is directed away from the origin
Correct Answer: C
Solution :
\[\vec{r}=\cos \omega t\,\hat{x}\,+sin\omega t\,\hat{y}\] \[\vec{v}=-\omega \sin \omega t\,\hat{x}+\omega \cos \omega t\,\hat{y}\] \[\vec{a}=-{{\omega }^{2}}\cos \omega t\,\hat{x}+\omega \sin \omega t\,\hat{y}=-{{\omega }^{2}}\vec{r}\] \[\vec{r}.\vec{v}=0\] hence \[\vec{r}\bot \vec{v}\]\[\vec{\alpha }\]is directed towards the origin.
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