A particle moves in the X-Y plane according to the equation `vecr=(veci+2vecj)Acosomegat`. The motion of the particle is

Options

A. (i), (ii)
B. (i), (iii)
C. (i), (iii), (iv)
D. (iii), (iv)

Answer

C

Explanation

`vecr=(hati+2hatj)Acosomegat`
`=Acosomegathati+2Acosomegathatj=xhati+yhatj`
`x=Acosomegat`, `y=2Acosomegat`
`y/x=2impliesy=2x` (straight line), (i) is O.K.
`(dvecr)/(dt)=(hati+2hatj)(-Aomegasinomegat)`
`veca=(d^2vecr)/(dt^2)=(hati+2j)(-Aomegacosomegat)=-omega^2vecr`
`vecaalpha-vecr(SHM)`, (iv) is O.K.
sin and cos are periodic functions, (iii) is O.K.