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The position vector of a particle is vec...

The position vector of a particle is `vec( r) = a cos omega t i + a sin omega t j`, the velocity of the particle is

A

directed towards the origin

B

directed away from the origin

C

parallel to the position vector

D

perpendicular to the position vector

Text Solution

Verified by Experts

The correct Answer is:
D
`vec r =( a cos omega t) hati + a sin (omega t) hatj`
`therefore` Slope of the position vector `=(a sin omega t)/(a cos omega t) = tan omega t` and velocity
`v=(dr)/(dt)=- (a omega sin omega t) hati +(a omega cos omega t) hat j`
`therefore` Slope of the velocity vector
`=-(a omega cos omega t)/(a omega sin omega t) = - cot omega t =-(1)/(tan omega t)`
Thus `(tan omega t) xx (-(1)/(tan omega t)) =-1`
Thus the velocity vector is perpendicular to the position vector.
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