A rod of mass $$m=23.75\text{ kg}$$ and length $$l=88.48\text{ cm}$$ is kept on a table with a quarter of its length over the table (see diagram). After being released, it tilts and then begins to slip from the edge of the table when it reaches the angle $$\theta_c = \arcsin(0.6)$$. Find the coefficient of friction between table and rod.

The answer is of the form $$\frac{A}{B}$$, where $$A$$ and $$B$$ are coprime positive integers. Find $$A+B$$.

Details and Assumptions:

• Take acceleration due to gravity $$g=9.8\text{ ms}^{-1}$$.
• The angle is measured clockwise from the horizontal.
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