A particle moves in the xy-plane under the action of a force F such that the components of its linear momentum p at any time t are `p_(x)=2cost`, `p_(y)=2sint`. The angle between F and p at time t is

Options

A. `90^(@)`
B. `0^(@)`
C. `180^(@)`
D. `30^(@)`

Answer

A

Explanation

`vec(p) p_(x)hat(i) + p_(y)hat(j) = 2cos t hat(i) + 2 sin t hat(j)`
`vec(F) = (dvec(p))/(dt) = -2 sin t hat(i) + 2cos t hat(j)`
`vec(F).vec(p) = 0" " i.e. theta = 90^(@)`