The time taken by an object to slide down a 45° rough inclined plane is n times the time it takes to slide down a perfectly smooth 45° inclined plane. The coefficient of kinetic friction between the object and the incline plane is:
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Question

The time taken by an object to slide down a 45° rough inclined plane is n times the time it takes to slide down a perfectly smooth 45° inclined plane. The coefficient of kinetic friction between the object and the incline plane is:

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G1 Physics · Accepted Answer

For the smooth plane, a₁ = g sin45° = g/√2. For the rough plane, a₂ = g(sin45° − μ cos45°) = (g/√2)(1−μ). For the same distance from rest, a₁t₁² = a₂t₂². Given t₂ = nt₁, so 1 = (1−μ)n². Hence μ = 1 − 1/n².