Center of Mass?

Classical Mechanics Level 2

A sphere and a hemisphere's flat surface is placed on the ground, such that the diameter of the sphere is equal to the radius of the hemisphere.

Which of them have a lower center of mass?

The hemisphere The sphere They both have an equal center of mass

Winston Choo by Winston Choo , 46, Singapore

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1 solution

David Vreken
Dec 15, 2018

The center of mass of the hemisphere flat on the ground with a radius of r h r_h is 3 8 r h \frac{3}{8}r_h above the ground (assuming an evenly distributed density).

Since the diameter of the sphere is equal to the radius of the hemisphere, the radius of the sphere r s r_s is r s = 1 2 r h r_s = \frac{1}{2}r_h , so the center of of mass of the sphere is r s = 1 2 r h r_s = \frac{1}{2}r_h above the ground.

Since 3 8 r h < 1 2 r h \frac{3}{8}r_h < \frac{1}{2}r_h , the center of mass of the hemisphere is lower than the sphere.

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