A uniform hoop of mass m and radius R rolls down an inclined plane of length I withoutslipping. The plane, which is originally horizontal, is lifted up at a constant rate such that theangle of the plane with the horizontal at time t is o = wt (see figure).RgO = 0 t(a) i. q and 0 are not independent. If 0 = 0 when q = 1, determine the relation betweenthem.ii. Determine the height of the centre of mass of the hoop above the base of the plane.iii. Hence show that the Lagrangian of the body, expressed in terms of the distance qfrom the pivotal point of the plane, isL = ma² +ms'q? – mg(a sin wt + Rcos wt).(b) Determine the Euler-Lagrange equations for the system.Note: you may assume the Lagrangian equations of motion for generalised co-ordinates q::d (OL

Given: The mass of the hoop is m and its radius is R. The given problem has two degrees of freedom.…

Answered: A uniform hoop of mass m and radius R…

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