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# A particle moves moved in the x-y plane under the action of a force vector F such that the value of its linear momentum vector P at anytina t is Px=2cost, Py=2sint.The angle between vector F and vector P at a given time to will be

2 years ago

Arun
25768 Points

Given:  Px= 2 cos t,

Py =2 sin t

P = Px i + Py j = 2 cos t i + 2 sin t j

Now according to the Newton's second law we can calculate components of forces using respective momentum component as:  F = dp/dt

Fx = - 2 sin t

Fy = 2 cos t

F =  Fx i + Fy j = -2 sin t i + 2 cos t j

Lets try to find out the dot product of F and P,

F P = 0 -------------(3)

but we do know that dot product of force and momentum can also be given in the form of angle between them as

F P = FP cos θ ---------------------(1)

Comparing both equations

⇒ θ = 90°

2 years ago
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