Save the rod

A rod of mass M\displaystyle{M} and length 2a\displaystyle{2a} is placed horizontally on the edge of a table. Initially, the centre of mass of the rod is at a distance of a/3\displaystyle{^a/_3} from the edge. The rod is released from the rest. The rod slips after it has turned through an angle θ\displaystyle{ \theta }. The coefficient of friction μ\displaystyle{\mu} between the rod and the table can be expressed as abtanθ.\dfrac{a}{b} \tan \theta. Find a+b.\displaystyle{a+b.}

Note

  • a a and b b are positive, co-prime integers.
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