Question

The position vector of a particle is $\overrightarrow{r}=\left(a\cos \omega t\right)\hat{i}+\left(a\sin \omega t\right)\hat{j}$. The velocity of the particle is

• A. Parallel to position vector
• B. Perpendicular to position vector
• C. Directed towards the origin
• D. Directed from away from the origin

Answer 1

The correct option is B Perpendicular to position vector

$r=\left(acos\omega t\right)i+\left(asin\omega t\right)j$.

Hence differentiating it, we get $v=$ $-\left(asin\omega t\right)i+\left(acos\omega t\right)j$.
If we take a dot product of these $2$, it comes $0$, hence, they are perpendicular to each other.