Gordon rule question Q#3 Two solid sphere simultaneously start rolling from rest

Question

Gordon rule question Q#3 Two solid sphere simultaneously start rolling from rest downan incline. One sphere has twice the radius and twice the mass ofthe other. Which sphere reaches the bottom of the incline first?.Which has the greatest speed at the bottom?. Which has the greatertotal kinetic energy at the bottom?      please explain in greatdetail. Gordon rule question Q#3 Two solid sphere simultaneously start rolling from rest downan incline. One sphere has twice the radius and twice the mass ofthe other. Which sphere reaches the bottom of the incline first?.Which has the greatest speed at the bottom?. Which has the greatertotal kinetic energy at the bottom?      please explain in greatdetail.

Explanation / Answer

The spheres will reach the bottom at the same time. This isbecause their moments of inertia are both given by the formula       I = ( 2 /5) M R2 Therefore the ratio between translational and rotationalkinetic energies will be the same. While the two spheres will havethe same speed when they reach the bottom, the larger sphere willhave the greater total kinetic energy on account of its greatermass.

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