Question

The position vector of a particle is

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

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

Answer 1

Answer: (B)

Perpendicular to the position vector

Answer 2

$\overrightarrow{r} = (a\cos\omega t)\widehat{i} + (a\sin\omega t)\widehat{j}$

$\overrightarrow{v} = \frac{d\overrightarrow{r}}{dt} = - a\omega\sin\omega t\widehat{i} + a\omega\cos\omega t\widehat{j}$

As $\overrightarrow{r}.\overrightarrow{v} = 0$ therefore velocity of the particle is perpendicular to the position vector.