Question

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 = 2 cost, p=2 sint. The angle between
Fand p at time tis [MP PET 1996; UPSEAT 2000]​

Answer 1

Px=2 cos t

Py=2sint

P= 2costi^+ 2 sintj^

F=dP/dt

Fx= -2sin¢

Fy= 2cos t

¢=90°

Answer 2

Explanation:

Force is defined as the rate of change of momentum.

Px  = 2cost

P y=2sint

P =2cost  i ^ +2sint  j ^

F=  dt /dP

Fx=−2sint

Fy =2cost

From law of vector dot product,

A.B =ABcosθ

Where θ is angle between them.

cosθ=  AB /a.b

Here,

cosθ=  FP/ F .P

cosθ=  FP −2cost×2sint+2cost+2sint

cosθ=0

θ=90°

i hope this will help you .

i tried my best

THANK YOU