The average density of Moon, if it contains solid rock of density
Answer to Problem 9Q
Solution:
Explanation of Solution
Given data:
The density of soil rock is
The density of water is
Formula used:
The expression for volume of a sphere is written as,
Here, r is the radius of the sphere.
The expression for density of an object is written as,
Here, M is the mass of the object.
Explanation:
Recall the expression for volume of a sphere to determine the volume of Moon (considering Moon to be a perfect sphere).
Here, r is the radius of Moon.
The volume of the sphere varies with
Here, subscript i represents the corresponding quantities for the inner portions of Moon.
The volume of the inner portion of Moon is,
Substitute
Substitute V for
So,
Here, the subscript o represents the corresponding quantity for the outer portion of Moon.
Substitute
The mass of the inner potion can be written as,
The mass of the outer portion is written as,
The total mass of Moon is written as,
Substitute
Substitute
Write the expression for density of Moon as,
Substitute
Substitute
Conclusion:
The density of Moon is
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Chapter 13 Solutions
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