A particle of mass `2kg` moves under a force given by
`vec(F)=-(8N//m)(xhat(i)+yhat(j))`
where `hat(i)` and `hat(j)` are unit vectors in the `x` and `y` directions.
The particle is projected from a point on `x` axis at `x=a` in `xy` plane with an initial velocity `vec(v)=v_(0)hat(j)`. Select correct statement (s). The particle will move in

Options

A. An elliptical path if `(v_(0))/a=3s^(-1)`
B. A circular path if `(v_(0))/a=5s^(-1)`
C. A circular path if `(v_(0))/a=2s^(-1)`
D. An elliptical path if `(v_(0))/a=1s^(-1)`

Answer

A, C, D

Explanation

For circular path amplitude of SHM along both axis must be same.
`v_(0)=aomega`