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AP Physics C: Mechanics
6.5 Rolling
6.1 Rotational Kinetic Energy
AdvancedMCQConceptual20.9k
A right triangle representing a fixed ramp inclined at an angle \(\theta\) to the horizontal ground. Near the top of the incline, two circles of equal radius \(R\) rest side by side along the incline surface. The upper-left circle has a solid gray interior, representing the solid sphere, labeled \(M\). The upper-right circle is an unfilled ring with a thin dark perimeter line, representing the hollow spherical shell, also labeled \(M\). A dashed line extends horizontally from the base of the ramp to indicate the angle \(\theta\) between the ground and the ramp surface. No other labels, lines, text, or axes appear.
Solid sphere and hollow spherical shell on an incline of angle \(\theta\).
A uniform solid sphere and a thin hollow spherical shell of identical mass \(M\) and radius \(R\) are released simultaneously from rest at the top of an incline of angle \(\theta\). Both spheres roll down the incline to the bottom without slipping, but the hollow spherical shell consistently takes a longer time to reach the bottom than the solid sphere. Which of the following explanations correctly accounts for this difference in travel time?

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