A particle moves so that its position vector is given by `vec r = cos omega t hat x + sin omega t hat y`, where `omega` is a constant which of the following is true ?

Options

A. Velocity and acceleration both are perpendicular to `vec(r)`
B. Velocity and acceleration both are parallel to `vec(r)`
C. Velocity is perpendicular to `vec(r)` and acceleration is directed towards the origin
D. Velocity is perpendicular to `vec(r)` and acceleration is directed away from the origin

Answer

C

Explanation

Position vector `vec(r)= cos omega t hat(x) + sin omega t hat(y)`
`vec(v) = - omega sin omega t hat(x) + omega cos omega t hat(y)`
`vec(a)= - omega^(2) cos omega t hat(x)- omega^(2) sin omega t hat(y)= - omega^(2) vec(r)`
`vec(r).vec(v) = 0` hence `vec(r) bot vec(v)`
`vec(a)` is directed towards the origin.