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Question

# A piece of ice starting from rest slides down a rough 45∘ incline in twice the time it takes to slide down a frictionless 45∘ incline. What is the coefficient of friction between the ice and incline?

A
0.25
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B
0.50
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C
0.75
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D
0.40
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Solution

## The correct option is C 0.75In both the case, the initial speed u and the distance s travelled is According to formula: s=ut+12at2 at2 is equal (as u=0 in both the cases). Let a1 be the acceleration of the ice block on rough incline and t1 be the time taken to slide down this rough plane. Similarly, let a2 and t2 be the similar quantities in case of frictionless inclined plane. Given that t1=2t2 Further, a1a2=t22t21 (∵at2= constant) ⇒a1a2=t224t22=14 ... (1) But a1=g(sinθ−μcosθ) ... (2) and a2=gsinθ ... (3) ∴g(sinθ−μcosθ)gsinθ=14 ⇒4sinθ−4μcosθ=sinθ ⇒3sinθ=4μcosθ ∴μ=34tanθ=34tan45∘⇒μ=34=0.75 Hence, the correct answer is option (c).

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