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.

(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.