Question

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

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

Answer 1

Answer: (B)

perpendicular to position vector

Position vector,
$r=\left(acos\omega \right)\hat{i}+\left(asin\omega \right)\hat{j}$
velocity $v=\frac{dr}{dt}$
$=\frac{d}{dt}\left[\right(acos\omega )\hat{i}+(asin\omega \left)\hat{j}\right]$
$(-acos\omega )\hat{i}+\left(asin\omega \right)\hat{j}$
$v\cdot r=\left[\right(-asin\omega )\hat{i}+(acos\omega \left)\hat{j}\right]\left[\right(-acos\omega )\hat{i}+(asin\omega \left)\hat{j}\right]$
$v\cdot r=0$
i.e., velocity vector is perpendicular to position vector.