There are two inclined surface of equal length (L) and same angle of inclination 4 5 ∘ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much t

Question

There are two inclined surface of equal length (L) and same angle of inclination 4 5 ∘ 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 ( μ k ​ ) between the object and the rough surface is close to :NEET 2025

TestHub · Accepted Answer

⇒ ⇒ ⇒ ⇒ ⇒ ​ L = 2 1 ​ a S ​ t S 2 ​ = 2 1 ​ a R ​ t R 2 ​ ( t R ​ t s ​ ​ ) 2 = a S ​ a R ​ ​ ( 2 1 ​ ) 2 = g sin θ g sin θ − μ k ​ g cos θ ​ 4 1 ​ = sin 4 5 ∘ sin 4 5 ∘ − μ k ​ cos 4 5 ∘ ​ 4 1 ​ = ( 2 ​ 1 ​ ) ( 2 ​ 1 ​ ) ​ ( 1 1 − μ k ​ ​ ) 4 1 ​ = 1 − μ k ​ ⇒ μ k ​ = 1 − 4 1 ​ = 4 3 ​ = 0.75 ​

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