# A Body Takes Time T To Reach The Bottom Of An Inclined Plane Of Angle θ Will The Horizontal. If The Plane Made Rough, Time Takes Now Is 2T. The Coefficient Of Friction Of The Rough Surface Is

The length of incline, s = $$\frac{1}{2}g sin\Theta t^{2} —[1]$$

The friction force, f =$$\mu N = \mu mg cos\Theta$$

a =$$(sin \Theta – \mu cos\Theta)g$$

Therefore,

s =$$\frac{1}{2} * (sin\Theta – \mu cos\Theta)g * (2t)^{2}—[2]$$

From both the equations, we have

$$sin\Theta = (sin\Theta – \mu cos\Theta)4$$

Therefore,$$\mu = \frac{3}{4}tan\Theta$$

The coefficient of friction of the rough surface is$$\frac{3}{4}tan\Theta$$

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