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Problem $16\mathrm{.}104-$ A drum attached to a disk and a cord

A drum of $4-$in$.$ radius is attached to a disk of $8-$in$.$ radius. The disk and drum have a total weight of $10\mathrm{.}00$ lb and a combined radius of gyration of $6$ in $.$ A cord is attached as shown and pulled with a force $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ of magnitude $5$ lb $.$ Know that the disk rolls without sliding.

Problem $16\mathrm{.}104.$b $-$ Minimum required coefficient of static friction

Determine the minimum value of the coefficient of static friction compatible with this motion. $($Round the final answer to three decimal places.$)$