A smooth block is released from rest on a 45º incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of f…

Question

A smooth block is released from rest on a 45º incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is-

Accepted Answer

Correct answer: C. (c) When fiction is absent a_1 = g sin θ ∴ s_1 = 12a_1t_1^2 ........ (i) When friction is present a_2 = g sin θ – μ g cos θ ∴ s_2 = 12a_2t_2^2 ........ (ii) From Eq. (i) and (ii) 12a_1t_1^2= 12a_2t^2_2 or a_1t_1^2 = a_2 (nt_1)^2 (∴ t_2 = nt_1) or a_1 = n^2a_2 or a_2a_1= g s i n θ−μ g c o s θg s i n θ= 1n^2 or g s i n 4 5 º−μ g c o s 4 5 ºg s i n 4 5 º= 1n^2 or 1 – μ_k = 1n^2 or μ_k = 1 – 1n^2

$A smooth block is released from rest on a 45º incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is-$

Solution

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