Question

Position vector of a particle is given by $\overrightarrow{r}=acos\omega t\hat{i}+asin\omega t\hat{j}$. Which of the following is/are true?

• A. velocity vector is parallel to position vector
• B. velocity vector is perpendicular to position vector
• C. acceleration vector is directed towards the origin
• D. acceleration vector is directed away from the origin

Answer 1

Answer: (B), (C)

The correct options are
B velocity vector is perpendicular to position vector
C acceleration vector is directed towards the origin

$\overrightarrow{r}=acos\omega t\hat{i}+asin\omega t\hat{j}$
$velocity=\overrightarrow{v}=\frac{d\overrightarrow{r}}{dt}=-a\omega sin\omega t\hat{i}+a\omega cos\omega t\hat{j}$
$Acceleration=\frac{d^2\overrightarrow{r}}{d{t}^2}=-a{\omega }^{2}cos\omega t\hat{i}-a{\omega }^{2}sin\omega t\hat{j}=-{\omega }^2\overrightarrow{r}$