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Chapter 13: Q23P (page 380)

One model for a certain planet has a core of radiusR and mass Msurrounded by an outer shell of inner radius R, outer radius 2R, and mass4M. IfM=4.1×1024kgandR=6.0×106m, what is the gravitational acceleration of a particle at points (a)R(b)3Rfrom the center of the planet?

Short Answer

Expert verified

a)Thegravitational acceleration of a particle at points R from the center of the planetis7.6 m/s2.

b)Thegravitational acceleration of a particle at points 3R from the center of the planet is4.2 m/s2

Step by step solution

01

Listing the given quantities

Mass of the planetM=4.1×1024kg

Radius of the planetR=6.0×106m

02

Understanding the concept of the gravitational acceleration

Here, by using the concept of the gravitational acceleration solve the given problem

Formula:ag=GMR2

03

Calculation of the gravitational acceleration of a particle at points from the center of the planet

(a)

The gravitational acceleration is

g=GMR2=7.6 m/s2

Thegravitational acceleration of a particle at points from the center of the planet is7.6 m/s2

04

Calculation of the gravitational acceleration of a particle at points 3R from the center of the planet

(b)

Note thatthetotal mass is5M. Thus,ag

ag=G(5M)(3R)2=4.2 m/s2

Thegravitational acceleration of a particle at pointsfrom the center of the planet is4.2 m/s2

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