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 prependicular 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 acceelration is directed away from the origin

Answer

C

Explanation

Hdrem ` vvec r = coa omega t hat x + sin omega t hat y` ….(i)
` velocity , `vec v = ( vec (dr)/(dt) =- omega sun omega t hat x + cos t hat y ` …(ii)`
Acceleration , `vec a =- omega cos omega t hat x - omega ^2 sin omega that y`
` =- omega^2 vec r` ....(iii)`
From (iii), we note that acclerated is directed towards the origin because ` vec a` is in opposite direction to `vec r` ltbrlt Here, ` ve3c v. vec r = ( -omega t hat x = omegat hat y)`
` =- omega sin omega t cos t + omega sin omega t cos omega t =0`
i.e. , `vec v ` and ` vec r` are peroendicular to each other.