Question

A solid sphere and a solid cylinder of equal radii and masses of 40kg and 32kg, respectively, roll together down an inclines plane from rest. Which reaches the bottom of the incline first?

Answer 1

Here , for solid sphere and solid cylinder

as the acceleration of the objects is inversely proportional to the moment of inertia

moment of inertia of solid sphere, Isph = 0.40 * m * R^2

moment of inertia of solid cylinder , Icyl = 0.50 * M * R^2

hence , as the radius of gyration of solid cylinder is more than the solid sphere

the acceleration of the solid sphere will be more than the acceleration of cylinder

hence , the solid sphere will reach the bottom first