Problem 3A hoop of mass m and radius R, rolls without slipping down an inelinedplane of angle a. The inclined plane of mass M moves horizontally. Let Xbe the abscissa of point O' with respect to 0, and s be the abscissa of thecenter of mass of the rolling hoop with respect to O'. Gi ven: the moment ofinertia of the hoop is I = mR², and the condition of rolling without slippingis expressed as s =RO:1. Write the Lagrangian of the system.2. Assuming that the Lagrangian of the system (inclined plane and hoop)is given by:1L = ms" +(m + M)X" + ms'X'cos(a) + mg(s)sin(a)3. Write the expression of the Lagrangian function4. Derive the Euler Lagrange equations5. Find s" and X" in terms of the masses (m,M), angle a and gReferencelevelm,R

As we already know that moment of inertia is said to be as mass of the body , when a body is…

Answered: Problem 3 A hoop of mass m and radius…

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