Two balls roll down an incline...?

Question

One ball is twice the diameter of the other and both have the same mass. Which ball will reach the bottom first?

By the way, this is not a homework question. I was actually asked this question during a job interview and was curious to if I got it right.

Answer 1

This is a Famous Galileo experiment.

They will roll at the same speed, as the size doesn't matter.
It is also actually the case that the mass also does not matter.

While Galileo proved this using experimentation, it can also simply be proven through logical theory:

If a Larger object moves faster than a small object, then a Huge one must move faster.

If you create a Huge object by combining a Large Object and a Small object, then you've combined a Slow object with a Fast object, to make an even Faster one.

If isn't possible that adding something slow to something fast would accelerate it beyond the faster of the two

Therefore, Objects must fall, Roll, accelerate at the same speed.

EDIT: The above poster would only be correct if the balls started lined up at the centre point, not the edge, which wouldn't really make sense to do. I'd assume both balls were starting with their frontmost edge equal

Answer 2

Sorry, insufficient data. If the centers of the balls start from the same distance up the plane. the larger will reach the bottom first. If the "leading point" of each ball starts from the same distance up the plane, both will take the same amount of time to reach a perpendicular erected from the bottom point on the plane. On the other hand, if reaching the bottom means touching the horizontal plane at the bottom of the incline, the smaller will reach the bottom first if the "leading points" start from the same perpendicular.

Answer 3

In a vacuum, both will reach the bottom at the same time. Gravity will provide the same acceleration.

Considering air, the smaller ball will roll faster, having less wind resistance.

Answer 4

What kind of job were you interviewing for?

Assuming the balls are both of uniform density, roll without slipping, and wind resistance is negligible, they will reach the bottom at the same time.

Answer 5

1. No, the ball rolling down the plane with the highest incline will reach the bottom first. 2. No 1 false 2True 3false

Answer 6

The moment of inertia of a thin walled hollow sphere is:
I = (2/3)MR^2
The moment of inertia of a solid sphere is:
I = (2/5)MR^2
Either way doubling the radius makes the moment of inertia four times as big.
With the same force acting on it, the smaller ball will reach the bottom first.

Answer 7

The smaller ball should reach the bottom first, smaller rotation speed. You can thank my brother.

Answer 8

In the absence of resistance, their centers have the same acceleration and velocity. However the front of the larger one will always be in ahead of the front of the smaller one, so the larger one should touch the ground first.

Answer 9

I think the one that is not twice the size in diameter. I think because its mass is in a smaller area....

Answer 10

Barring air resistance, etc. they both will reach at same time.