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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