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80. (a) Since the volume of a sphere is 4
π
R
3
/3, the density is
total
total
33
4
3
3
.
4
MM
R
R
ρ
ππ
==
When we test for gravitational acceleration (caused by the sphere, or by parts of it) at
radius
r
(measured from the center of the sphere), the mass
M
which is at radius less than
r
is what contributes to the reading (
GM/r
2
). Since
M
=
(4
π
r
3
/3) for
r
≤
R
then we can
write this result as
3
total
3
total
23
3
4
43
M
r
G
R
GM
r
rR
π
§·
¨¸
¨
¸
©¹
=
when we are considering points on or inside the sphere. Thus, the value
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 Spring '08
 Any
 Physics, Acceleration, Mass

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