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Chapter 1: Q2DQ (page 424)

If all planets had the same average density, how would the acceleration due to gravity at the surface of a planet depend on its radius?

Short Answer

Expert verified

Radius of planet will be directly proportional to acceleration due to gravity.

Step by step solution

01

Concept of density

Defining density is a matter of mass divided by volume.

ρ=MV

02

Determination of the relation between radius of planet with acceleration due to gravity.

g=GMR2……….. (i)

Substitute equation (i) in density equation,

g=G×ρ×VR2V=43πR3g=G×ρ×43×π×R3R2g=43ρπGR

Thus, from above equation we can say that radius of planet is directly proportional to acceleration due to gravity.

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