Question

A thin light string is wrapped around a solid uniform disk of mass M and radius...

A thin light string is wrapped around a solid uniform disk of mass M and radius R, mounted as shown. The loose end of the string is attached to the axle of a solid uniform disc of mass m and the same radius r which is can roll down without slipping down an inclined plane that makes angle θ with the horizontal. Find the acceleration a of the rolling disc. Neglect friction in the axle of the pulley.
a = (2mg sin θ)/(2M + 3m)
a = (mg cos θ)/(M + 3m)
a = (2mg sin θ)/(M + 2m)
a = (2mg sin θ)/(M + 3m)
a = (mg cos θ)/(2M + m)

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