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A given object takes 3 times a much time to slide down a $45 °$ rough incline as it takes to slide down a perfectly smooth $45 °$ incline. The coefficient of kinetic friction between the object and the incline is given by

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$\frac{1}{9}$

$\frac{1}{3}$

$\frac{8}{9}$

$\frac{2}{9}$

answer is C.

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Detailed Solution

$μ = \tan θ (1 - \frac{1}{n^{2}}) = 1 - \frac{1}{n^{2}} [As θ = 45^{\circ}]$

$= 1 - \frac{1}{3^{2}} = \frac{8}{9}$

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