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°
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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
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