Aditya's challenges in Mechanics 7

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.