Which Mass Reaches the Bottom First When Rolling Down an Incline?

[hatingphysics]

The five masses below all have the same radius and a cylindrically symmetric mass distribution. They start to roll down an inclined plane, starting from rest, at the same time and from the same height. Give their order of arrival at the bottom.

Icm=684 g*cm2, M = 47g

Icm=373 g*cm2, M = 41g

Icm=415 g*cm2, M = 44g

Icm=600 g*cm2, M = 50g

I found the ratio by dividing inertia/mass. I thought it was the one with the lowest ratio reaches the bottom first...but why am I not getting the right answers?!

 

[member 553083]

The correct order is: Icm=373 g*cm2, M = 41g, Icm=415 g*cm2, M = 44g, Icm=600 g*cm2, M = 50g, Icm=684 g*cm2, M = 47g. The order of arrival is determined by the moment of inertia of each mass. The lower the moment of inertia, the faster the mass will reach the bottom. Moment of inertia is calculated by dividing the mass by the radius of the cylindrical body. Therefore, the mass with the lowest moment of inertia (Icm=373 g*cm2, M = 41g) will arrive first, followed by the mass with the second lowest moment of inertia (Icm=415 g*cm2, M = 44g), and so on.