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In the figure, a small $0\mathrm{.}200$ kg block slides down a frictionless surface through height $h=0\mathrm{.}881m$ and then sticks to a uniform vertical rod of mass $M=0\mathrm{.}400kg$ and length $d=2\mathrm{.}22m.$ The rod pivots about point $O$ through angle $$ before momentarily stopping. Find $.$

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