Question

The position vector of a particle is $\overrightarrow{r}=a[\text{cos}\omega t\hat{i}+\text{sin}\omega t\hat{j}]$. The velocity of the particle is

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

Answer 1

The correct option is D perpendicular to position vector.

$\overrightarrow{r}=a\left\{\right(cos\omega t)\hat{i}+(\text{sin}\omega t\left)\hat{j}\right\}$
$\therefore \overrightarrow{v}=a\{-\text{sin}\omega t\times \omega \hat{i}+\text{cos}\omega t\times \omega \hat{j}\}$
$\overrightarrow{r}.\overrightarrow{v}=a^2\omega \text{cos}\omega t\times -\text{sin}\omega t$
$+a^2\omega \text{sin}\omega t\times \text{cos}\omega t=0$
$\therefore \overrightarrow{r}\perp \overrightarrow{v}$