Assuming that the gravitational acceleration inside a homogeneous spherical shell is zero, show that the gravitational acceleration inside a homogenous uniform solid sphere is proportional to the distance from its center.

Assuming that the gravitational acceleration inside a homogeneous spherical shell is zero, show that the gravitational acceleration inside a homogenous uniform solid sphere is proportional to the distance from its center.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter5: Gravitation

Section: Chapter Questions

Problem 5.6P: Compute directly the gravitational force on a unit mass at a point exterior to a homogeneous sphere...

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

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Assuming that the gravitational acceleration inside a
homogeneous spherical shell is zero, show that the
gravitational acceleration inside a homogenous
uniform solid sphere is proportional to the distance
from its center.

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