Solution - American Association of Physics Teachers

2013 F = ma Exam 910. Which of the following can be used to distinguish a solid ball from a hollow sphere of the same radius and mass?(A) Measurements of the orbit of a test mass around the object.(B) Measurements of the time it takes the object to roll down an inclined plane.(C) Measurements of the tidal forces applied by the object to a liquid body.(D) Measurements of the behavior of the object as it floats in water.(E) Measurements of the force applied to the object by a uniform gravitational field.SolutionThe measurement described in (B) is certainly appropriate; the solid ball has a smaller moment of inertiathan the hollow sphere and will accelerate down the inclined plane faster.The measurements in (A) and (C) are unhelpful because they only probe the gravitational field outside theobject; for a spherically symmetric object this depends only on the mass. The force measured in (E) dependsonly on the object’s total mass; the buoyant force applied in (D) depends only on the external shape of theobject.Copyright c○2013 American Association of Physics Teachers