Variable Friction on horizontal Rod !!

Let a uniform rod of mass MM and length LL is rotating with angular velocity ω\omega about an point PP which is at the position of xx from one end of rod . At time zero, the rod is placed gently on a rough, level surface having coefficient of friction μ\mu .

If the total time taken by the rod to stop completely TT, then for different values of position xx, the time taken by the rod in various experiments are different.

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

100×TminTmax100\quad \times \quad \cfrac { { T }_{ min } }{ { T }_{ max } } .


Details

  • L L = 10 m
  • MM = 10 kg
  • μ\mu = 0.5
  • gg = 10 m/s^2
  • ω\omega = 10 rad/s
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