The Mass Density of a Certain Planet Has Spherical Symmetry

question 27

Multiple Choice

The mass density of a certain planet has spherical symmetry but varies in such a way that the mass inside every spherical surface with center at the center of the planet is proportional to the radius of the surface.If r is the distance from the center of the planet to a point mass inside the planet, the gravitational force on the mass is:

• A)not dependent on r
• B)proportional to r²
• C)proportional to r
• D)proportional to 1/r
• E)proportional to 1/r²

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Definitions:

Returns to Scale

The rate at which output changes if the scale of all inputs is changed by the same proportion.

Output Level

The amount of product or service that is produced by a company or an economy at a given time.

Isoquants

Curves representing combinations of inputs which yield the same level of output in production theory, illustrating technical substitution and factor combinations.

MRTS

Marginal Rate of Technical Substitution; the rate at which one input must increase when another input decreases to keep output constant.