Position vectors of a particle moving in xy plane at time t is `vecr=a(1-cos ometat)hati+asin omegat hatj`. The path of the particle is

Options

A. a circle of radius a and center at (a,0)
B. a circle of radius a and center at (0,0)
C. an ellipse
D. neither a circle nor an ellipse

Answer

a

Explanation

Particle is moving in a circle of radius 'a' and centre (a,0) with constant angular velocity `' omega'`. At time t=0 particle is at origin and it starts rotating clockwise. At time t it has rotated an angle `theta` given by:
`theta=omegat`
`y=asin theta=a sin omegat`
and `x=a-acos theta=a(1-cos omegat)`
`:. vecr=a(1-cos omegat)hati+asin omegat hatj`