GATE PH 2025 PH Q64: Lagrangian Formulation

A wheel of mass

and radius

is made of a thin uniform distribution of mass

at the rim and a point mass

at the center. The spokes of the wheel are massless. The center of mass of the wheel is connected to a horizontal mass rod of length

, with one end fixed to O, as shown in the figure. The wheel rolls without slipping on horizontal ground with angular speed

. If

is the total angular momentum of the wheel about O, then the magnitude

. The value of

(in integer) is _____.

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