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PhysicsNEET 2025Friction: static, kinetic, rolling

Laws of Motion

There are two inclined surfaces of equal length LL and the same angle of inclination 45∘45^\circ 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 the rough surface as the smooth surface. The coefficient of kinetic friction (μk\mu_k) between the object and the rough surface is close to:

  1. A.0.25
  2. B.0.40
  3. C.0.5
  4. D.0.75✓

Solution

Smooth: a1=gsin⁡45∘a_1 = g\sin45^\circ. Rough: a2=g(sin⁡45∘−μcos⁡45∘)a_2 = g(\sin45^\circ - \mu\cos45^\circ). Same distance, t2=2t1⇒a2=a1/4t_2 = 2t_1 \Rightarrow a_2 = a_1/4, so 1−μ=14⇒μ=0.751 - \mu = \frac14 \Rightarrow \mu = 0.75.

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