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Solved: Applying Gauss’s Law for Gravitation. Using
Chapter 22, Problem 60P(choose chapter or problem)
CP Applying Gauss's Law for Gravitation. Using Gauss's law for gravitation (derived in part (b) of Problem ), show that the following statements are true: (a) For any spherically symmetric mass distribution with total mass
, the acceleration due to gravity outside the distribution is the same as though all the mass were concentrated at the center. (Hint: See Example
in Section 22.4.) (b) At any point inside a spherically symmetric shell of mass, the acceleration due to gravity is zero. (Hint: See Example 22.5.) (c) If we could drill a hole through a spherically symmetric planet to its center, and if the density were uniform, we would find that the magnitude of \(\bar{g}\) is directly proportional to the distance
from the center. (Hint: See Example
in Section 22.4.) We proved these results in Section
using some fairly strenuous analysis; the proofs using Gauss's law for gravitation are
easier.
Equation transcription:
Text transcription:
\bar{g}
Questions & Answers
QUESTION:
CP Applying Gauss's Law for Gravitation. Using Gauss's law for gravitation (derived in part (b) of Problem ), show that the following statements are true: (a) For any spherically symmetric mass distribution with total mass
, the acceleration due to gravity outside the distribution is the same as though all the mass were concentrated at the center. (Hint: See Example
in Section 22.4.) (b) At any point inside a spherically symmetric shell of mass, the acceleration due to gravity is zero. (Hint: See Example 22.5.) (c) If we could drill a hole through a spherically symmetric planet to its center, and if the density were uniform, we would find that the magnitude of \(\bar{g}\) is directly proportional to the distance
from the center. (Hint: See Example
in Section 22.4.) We proved these results in Section
using some fairly strenuous analysis; the proofs using Gauss's law for gravitation are
easier.
Equation transcription:
Text transcription:
\bar{g}
ANSWER:Solution 60P
Step 1
