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A $9-$kg uniform disk is attached to the $5-kg$ slender rod $AB$ by means of frictionless pins at $B$ and $C.$ The assembly rotates in a vertical plane under the combined effect of gravity and of a couple $M$ which is applied to rod $AB.$ At the instant shown, the assembly has an angular velocity of $6ra\frac{d}{s}$ and an angular acceleration of $30ra\frac{d}{s^2},$ both counterclockwise.

Determine the couple $M.$

The couple $M$ is N$-$m