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.
Answer & explanation
Correct answer: option 2
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.