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14.49:
a) At
,
0
=
r
the model predicts
3
m
kg
700
,
12
=
=
A
ρ
and at
,
R
r
=
the model
predicts
.
m
kg
10
3.15
m)
10
37
.
6
)(
m
kg
10
50
.
1
(
m
kg
700
,
12
3
3
6
4
3
3
×
=
×
×

=

=

BR
A
b), c)
∫
∫

=

=

=
=
R
BR
A
πR
BR
AR
π
dr
r
Br
A
π
dm
M
0
3
4
3
2
4
3
3
4
4
3
4
]
[
4
×
×

×
=

4
m)
10
37
.
6
)(
m
kg
10
50
.
1
(
3
m
kg
700
,
12
3
m)
10
37
.
6
(
4
6
4
3
3
3
6
π
kg,
10
99
.
5
24
×
=
which is within 0.36% of the earth’s mass.
d) If
m
)
(
r
is used to denote the mass
contained in a sphere of radius
,
r
then
.
)
(
2
r
r
Gm
g
=
Using the same integration as
that in part (b), with an upper limit of
r
instead of
R
gives the result.
e)
)
kg
m
N
10
673
.
6
(
)
(
,
at
and
,
0
at
0
2
2
11
2
⋅
×
=
=
=
=
=

R
R
Gm
g
R
r
g
r
g
.
s
m
85
.
9
m)
10
(6.37
kg)
10
99
.
5
(
2
2
6
24
=
×
×
f)
;
2
3
3
4
4
3
3
4
2

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