Consider four round bodies of same mass 33 kg and of the same radius 9.2 cm but

Question

Consider four round bodies of same mass 33 kg and of the same radius 9.2 cm but of different geometries - a solid sphere, a spherical shell, a solid cylinder, and a cylindrical shell. All four bodies roll without slipping down the same inclined plane. All four bodies start at zero initial velocity at the same distance from the bottom of the incline. Which body reaches the bottom first? All four take the same time. The cylindrical shell. The spherical shell. The solid sphere. Depends on the steepness of the incline. The solid cylinder.

Explanation / Answer

the one that finishes first has the greatest acceleration. this will be the one with the smallest moment of inertia.

solid sphere: .4mr2

thin sphere: .66mr2

solid cylinder: .5mr2

hollow cylinder: .5mr2

the solid sphere has the least inertia to overcome, and will consequently accelerate the fastest, reaching the bottom first

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