PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A solid disc, a thin circular ring, and a solid sphere each have the same mass 2.0kg and the same radius 0.20m. They are released simultaneously from rest at the top of identical smooth inclined planes of height 1.5m and roll down without slipping.
(a) Write the standard expressions for the moments of inertia of the disc, the ring, and the sphere about their central symmetry axes.
(b) Derive an expression for the linear acceleration of a rigid body of mass M, radius R, and moment of inertia I that rolls down an incline of angle θ without slipping.
(c) Using the expression obtained in part (b), determine the acceleration of each of the three bodies when the incline makes an angle of 30∘ with the horizontal.
(d) Hence arrange the three bodies in order of the time taken to reach the bottom and justify your answer on the basis of their distribution of mass.