Two cylinders (one hollow, one solid) made of linear elastic materials with the same outer diameter and length are subjected to the same external torque. neither cylinder breaks at this torque. which cylinder has the greater twist angle at this torque?

The hollow cylinder, because this has greater inertia, due to the distance of the mass from its center. Studying this solids in revolution, you will find that inertia is an important part here, because it change speed and resistance of this objects.

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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