Question
Download Solution PDFThere are two inclined surfaces of equal length (L) and same angle of inclination 45° with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction (μₖ) between the object and the rough surface is close to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCorrect option is : (4) 0.75
The equation for the rough and smooth surfaces is given by:
trough = 2tsmooth
Also, asmooth = g sin θ
The time taken is related as:
t ∝ 1/√a ⇒ tsmooth ∝ 1/√asmooth
arough ∝ g sin θ - μk g cos θ
We have:
trough / tsmooth = 2
Substitute the values for acceleration:
g sin θ / (g sin θ - μk g cos θ) = 2
⇒ (sin θ) / (sin θ - μk cos θ) = 4 ⇒ 1 / √2 = μk × 1 / √2
⇒1 - μk = 1 / 4
⇒ μk = 3 / 4 = 0.75
Last updated on Jun 16, 2025
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