A disc is purely rolling down an inclined plane of length ‘l’ & angle θ. What is the value of friction acting on it? Let the mass of the disc be M & radius be R.

A disc is purely rolling down an inclined plane of length ‘l’ & angle θ. What is the value of friction acting on it? Let the mass of the disc be M & radius be R. Correct Answer (Mgsinθ)/3

Let the angular acceleration of the disc be ‘α’. And the linear acceleration along the incline be ‘a’. For pure rolling, a = Rα. Mgsinθ – f = Ma———-(1), where f is the friction. fR = Iα————–(2), where I is the moment of inertia = MR2/2. fR = Ia/R, we substitute the value of a into the first equation, Mgsinθ – f = (MfR2)/( MR2/2) = 2f ∴ Mgsinθ – f = 2f Or f = (Mgsinθ)/3.
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