The objects described below all have the same mass. The cube has edge lengths R

Question

The objects described below all have the same mass. The cube has edge lengths R and is allowed to slide from rest down an inclined ramp. Friction between the cube and the ramp is sufficiently small that you may ignore it. The other objects have the same radius R and are allowed to roll from rest the same distance down the same ramp. Some friction is necessary for each object to roll on the ramp. Assume that there is adequate friction to allow rolling. With some thought you can see that this friction does no work as the objects roll and therefore won't complicate your analysis. Order the various objects from first to last by the time each requires to reach the bottom of the ramp. Cube Thin Hoop Cylinder Sphere

Explanation / Answer

As we know for the body rolling

net kinetic energy=0.5*mv^2 +0.5*I*w^2

also v=wr

since they are coming from same height ,initial potential energy of all bodies are same .

Since at the bottom also ,energy will be same for all bodies as no energy is lost during friction

So more is the moment of inertia,less will be velocity at the bottom so more time it will take

but for cube ,no rotation so it will come first

followed by cylinder ,sphere(if hollow sphere),and thin hoop

so order is

cube>cylinder>hollow sphere>thin loop

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