A particle moving in the x-y plane is subject to a central force F = f(r)Ã, wherer = √x² + y² and F = cos x + sin 0ỹ.=(i) Write the velocity in terms of the polar coordinates r and 0, and thus find anexpression for the angular momentum of the particle about the origin, alsoin terms of the polar coordinates.(ii) Show explicitly that the angular momentum is a constant of the motion.(iii) Derive an expression for the area dA swept out by the particle's positionvector r during a small time interval dt (during which its angular displace-ment is de). Hence show that dA/dt is constant (Kepler's Third Law).

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Answered: A particle moving in the x-y plane is…

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