arellano (aa39398) – Homework 1 – Weathers – (17101)
1
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printout
should
have
9
questions.
Multiplechoice questions may continue on
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before answering.
001
10.0 points
The
mass
of
the
planet
Saturn
is
about
5
.
64
×
10
26
kg and its radius 6
×
10
7
m.
Calculate its density.
Correct answer: 623
.
357 kg
/
m
3
.
Explanation:
Let :
M
= 5
.
64
×
10
26
kg
and
R
= 6
×
10
7
m
.
Assuming Saturn to be a sphere (neglecting
the rings),
V
=
4
3
π R
3
,
so the density of Saturn is
ρ
=
M
V
=
M
4
3
π R
3
=
3 (5
.
64
×
10
26
kg)
4
π
(6
×
10
7
m)
3
=
623
.
357 kg
/
m
3
.
002
10.0 points
A rope has a cross section
A
= 9
.
66 m
2
and
density
ρ
= 1690 kg
/
m
3
. The linear density
of the rope
μ
, defined to be the mass per unit
length, can be written in the form
μ
=
ρ
x
A
y
.
Based on dimensional analysis, determine
the powers
x
and
y
by choosing an expression
below.
1.
μ
=
ρ
A
2
2.
μ
=
1
ρ A
3.
μ
=
A
ρ
4.
μ
=
A
ρ
2
5.
μ
=
1
ρ A
2
6.
μ
=
ρ A
2
7.
μ
=
A
2
ρ
2
8.
μ
=
ρ
A
9.
μ
=
A
2
ρ
10.
μ
=
ρ A
correct
Explanation:
[
x
] means ”the units of
x
”.
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 Fall '10
 Weathers
 Acceleration, Mass, Work, Velocity, 10 m

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