A rigid body of mass M and radius R rolls without slipping on an inclined plane of inclination θ , under gravity. Match the type of body Column I with magnitude of the force of friction Column II. Column I Column II A) For ring I) M g sin θ 2 . 5 B) For solid sphere II) M g sin θ 3 C) For solid cylinder III) M g sin θ 3 . 5 D) For hallow cylinder IV) M g sin θ 2

Step-by-step solution

if a is the acceleration of the center of mass of the rigid body and f the force of friction between the sphere and the plane, the equation of translatory and rotatory motion of the rigid body will be, M g sin θ - f = M a ⇒ f = M α R + f and the relation between the moment of inertia and friction force, f × R = I α ⇒ α = f × R I , ⇒ M g sin θ = M f × R 2 I + f ⇒ f = M g sin θ M R 2 I + 1 The value of the moment of inertia of solid sphere, I = 2 5