A particle moves so th at its p o sitio n vector is `omega` Where is a constant which of the following is true

Options

A. velcocity and acceleration both are perpendicular to `vecr`
B. velocity and acceleration both are parallel to `vec r`
C. velocity is perpendicualr to `vec r` and acceleratio is directed towards the origin
D. velcocity is perpendicular to `vec r` and acceleration is directed away from the origin

Answer

B

Explanation

velocity and acceleration both are parallel to `vec( r)`
Here `vec(r ) = cos epsilon hat( x) =- epsilon t hat( x) + epsilon hat(y )`
Acceleration `vec( a) = (d v)/(d t) =- epsilon^(2) cos t hat( x )`
`vec( a) = - epsilon ^(2) [ cos epsilon t hat( x) + sin epsilon hat(y )` Here `vec( v) . vec( r ) = cos epsilon t hat( x ) + sin epsilon hat( y )`
`=- epsilon cos epsilon t sin epsilon t + epsilon t sin epsilon t`
`vec( v ) _|_ vec( r )`