Question

A particle is moving in x-y plane under the influence of force F At any time t value of the linear
momentum P is P. = 2 cost. P, = 2sint. Angle 0 between P and F at any time t will be
b) 30
A hullas suspended by a string from the ceiling of
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Answer 1

Answer:

90 degrees

Explanation:

for the particle question:

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