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.

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