Variable Friction on horizontal Rod !!

Let a uniform rod of mass \(M\) and length \(L\) is rotating with angular velocity \(\omega \) about an point \(P\) which is at the position of \(x\) from one end of rod . At time zero, the rod is placed gently on a rough, level surface having coefficient of friction \(\mu \).

If the total time taken by the rod to stop completely \(T\), then for different values of position \(x\), the time taken by the rod in various experiments are different.

Suppose the maximum possible time taken for the rod to slow is \({ T }_{ max }\) and the minimum possible time is \({ T }_{ min }\), find the value of :

\(100\quad \times \quad \cfrac { { T }_{ min } }{ { T }_{ max } } \).


Details

  • \( L\) = 10 m
  • \(M\) = 10 kg
  • \(\mu \) = 0.5
  • \(g\) = 10 m/s^2
  • \(\omega \) = 10 rad/s
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