# 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