A particle moves in the x-y plane under is influence of a force such that its linear momentum is `vec(P)(t)=A[hat(i)cos (kt)-hat(j)sin (kt)]`, where A and k are constants Angle between the force and the momentum is:

Options

A. `0^(@)`
B. `30^(@)`
C. `45^(@)`
D. `90^(@)`

Answer

D

Explanation

`vec(P)(t)=A[hat(i)coskt-hat(j)sin kt]`
`:.vec(F)(t)=(dvec(P))/(dt)=Ak[-hat(i)sin kt-hat(j)cos kt]`
`:.vec(F).vec(P)=A^(2)k[-sinktcoskt+sin kt coskt]`
`vec(F).vec(P)=0`
`rArr theta=90^(@)`