Before you are two balls, one solid and one hollow. They are to all appearences completely identical: same size, same weight, same outer material (though one might assume, correctly, that the hollow ball would need a higher-density material on the inside to make it the same weight).

Without breaking either of the balls, how can you easily determine which is hollow?

Assume that the material is solid enough that a hitting the side of the hollow ball will not result in any noticeable echo or vibrations.

(In reply to correction by dan)

I'm afraid your ignorance cannot save you. I suggest you go and look up rotational motion in an elementary physics book.

What you say can only be applied if the items don't roll. That is why physics problem posed for TRANSALATION motion always use "a block of mass M." That's because blocks cannot roll.

BUT! Get this, spheres roll. So you have to take rotational motion into account. And when things roll, it's moment of inertia that matters, not mass (although mass affects moment of inertia).

And for someone who understands physics (perhaps not you Dan), they can easily see that the answer is correct. It's pretty obvious that the simple difference between the two balls is moment of inertia. So anything that involves rolling/rotating the balls will show which one is hollow.

And just to show why you're wrong. Your reasoning is that gravity is the same for both balls. Again, for translational motion, you are correct. But you need to keep in mind that this is translational AND rotational motion. You need to include angular acceleration as well as regular acceleration.

T=I*alpha
T=net torque, I=moment of inertia, alpha=angular acceleration

The net torque is the same because of gravity and assuming they have the same friction. But because the moment of inertia is different, they will have different angular accelerations.

It is possible to use F=ma and T=I*alpha to show that I am correct. But it is a lot more complicated because the ball will roll with slipping in the beginning (v is not equal to r*w). My equations assumed that at the bottom, the balls roll without slipping (v=r*w). This can easily be done by getting a long enough incline. It's possible to find an expression to show "how long" is necessary. But in reality, trial and error may be simpler.

Edited on March 27, 2005, 5:38 am

Posted by np_rt on 2005-03-26 18:31:21