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. If $M = 4.1 \times 10^{24} k g$ and $R = 6.0 \times 10^{6} m$ , 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 planetis $7.6 m / s^{2}$ .

b)Thegravitational acceleration of a particle at points 3R from the center of the planet is $4.2 m / s^{2}$

Step by step solution

Listing the given quantities

Mass of the planet $M = 4.1 \times 10^{24} k g$

Radius of the planet $R = 6.0 \times 10^{6} m$

Understanding the concept of the gravitational acceleration

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

Formula: $a g = \frac{G M}{R^{2}}$

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

(a)

The gravitational acceleration is

$\begin{array}{rcl} g & = & \frac{G M}{R^{2}} \\ = & 7.6 m / s^{2} \end{array}$

Thegravitational acceleration of a particle at points from the center of the planet is $7.6 m / s^{2}$

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

(b)

Note thatthetotal mass is5M. Thus, $a g$

$\begin{array}{rcl} a g & = & \frac{G (5 M)}{{(3 R)}^{2}} \\ = & 4.2 m / s^{2} \end{array}$

Thegravitational acceleration of a particle at pointsfrom the center of the planet is $4.2 m / s^{2}$

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Short Answer

Step by step solution

Listing the given quantities

Understanding the concept of the gravitational acceleration

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

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

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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

Step by step solution

Listing the given quantities

Understanding the concept of the gravitational acceleration

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physical Quantities And Units

Fundamentals of Physics

Particle Model of Matter

Conservation of Energy and Momentum

Electricity and Magnetism

Space Physics

Study anywhere. Anytime. Across all devices.