Question

A particle moves in X-Y plane under the action of forces F such that the values of linear momentum p at any times is px​=2cost and py​=2sint. The angle between F and p​ at the time t will be:

(A) θ = 0°
(B) θ = 30°
(C) θ = 90°
(D) θ = 180°​

Answer 1

Answer:

From Newtons second law,

Force F is nothing but rate of change of momentum.

Hence,  F = dP/dt

Given, Px = 2cost  &  Py = 2sint

=> Fx = -2sint   &   Fy = 2cost

Now to find the angle between the force vector and the momentum vector, let us first find the dot product of these two vectors.

F.P = FxPx + FyPy

      = 2cost*-2sint + 2sint*2cost

      = -4cost*sint + 4cost*sint

      =  0

Also, F.P = |F||P|cosθ

=>  cosθ = 0

=>  θ = 90 degrees.

Hence, the angle between force and momentum vectors is 90 degrees