InterviewSolution
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InterviewSolution
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A smooth block is released at rest on a `45^(@)` 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 isA. `mu_(s)=1-1/(n^(2))`B. `mu_(s)=sqrt(1-1/(n^(2)))`C. `mu_(k)=1-1/(n^(2))`D. `mu_(k)=sqrt(1-1/(n^(2)))` |
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Answer» Correct Answer - C When fiction is absent `a_(1)=g sin theta` `:. S_(1)=1/2 a_(1)t_(1)^(2)`......(i) When friction is present `a_(2)= g sin theta-mu g cos theta` `:. S_(2)=1/2 a_(2)t_(2)^(2).....(ii)` From eq.(i) and (ii) `1/2 a_(1)t_(1)^(2)=1/2a_(2)t_(2)^(2)` or `a_(1)t_(1)^(2)=a_(2)(nt_(1))^(2) ( :. t_(2)=nt_(1))` or `a_(1)=n^(2)a_(2)` or `(a_(2))/(a_(1))=(g sin theta-mu g cos theta)/(g sin theta) =1/(n^(2))` or `(g sin 45^(@)-mu g cos 45^(@))/(g sin 45^(@))=1/(n^(2))` or `1-mu_(k)=1/(n^(2)) rArr ` or `mu_(k)=1-1/(n^(2))` |
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