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) = (d vec(p))/(dt) = A[ hat(i) ( - sin kt - hat(j) (cos t)k)]`
`vec(p) . vec(F) = 0` , i.e. angle between `vec(p)` and `vec(F) is 90^(@)`