When an object is rolling down a ramp, its energy is made up of three components:

ππβ=1/2ππ£^2+12πΌπ^2

The first term is the potential energy; this is the energy is takes to lift the object up the ramp. This is equal to ππβ with πm being the mass, π the acceleration due to gravity, and β the height of the ramp.

The second term is the translational kinetic energy; this is the energy it takes for the object to move down the ramp.

The third term is the rotational kinetic energy; this is the energy it takes for the object to roll. This is equal to 1/2πΌπ^2, with πΌ being the moment of inertia (the objectβs resistance to being rotated) and π being the angular velocity.

For the hollow cylinder, the mass is placed the farthest from the center and thus π is large, πΌ is large, and consequently it is slow. For the case of the solid cylinder, the mass distribution occurs more closer to the center, thus has lower πΌ and highest velocity.

**Thus, the solid cylinder reaches the bottom first.**

If you want to practice more questions like this, check out these other moment of inertia problems!

Here are some other tricky questions:

I think they should reach the bottom at the same time