A particle moves in the X-Y plane under the influence of a force such that its linear momentum is `oversetrarrp(t)=A[haticos(kt)-hatjsin(kt)]`, where A and k are constants. The 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) cos (kt) - hat(j) sin (kt)]`
`vec(F) = (dvec(p))/(dt) = Ak [- hat(i) sin (kt) - hat(j) cos (kt)]`
`vec(F).vec(p) = Fp cos theta` But`vec(F).vec(p) = 0 rArr cos theta = 0 rArr theta = 90^(@)`