Problem 1.42 [Difficulty: 2]
Given: Standard American golf ball: 1) to(20in.01.068.1
1) to(20oz01.062.1
±=
±
=
D
m
Find: Density and specific gravity; Estimate uncertainties in calculated values.
Solution: Density is mass per unit volume, so
()
() ()
3
3
3
3
3
3
333
3
4
kg/m 1130
m0254.0
in.
oz 16
kg 4536.0
in.68.1
1
oz 62.1
6
6
2
4
3
=××××=
====
π
ρ
ππ
π
ρ
D
m
D
m
R
m
V
m
and 13.1
kg 1000
m
m
kg
1130SG 3
3
OH2
=×==
ρ
ρ
The uncertainty in density is given by
2
1
22
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
∂
∂
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
∂
∂
=Dm u
D
D
u
m
m
u
ρ
ρ
ρ
ρ
ρ
%595.0
68.1
1.0
;3
6
3
6
3
%617.0
62.1
01.0
;1
1
44 ±=
±
=−=−=
⎟
⎠
⎞
⎜
⎝
⎛−⋅=
∂
∂
±=
±
==
∀
∀
=
∀
=
∂
∂
D
m
u
D
m
D
mD
D
D
u
m
m
m
ρ
π
π
ρ
ρ
ρ
ρ
ρ
ρ
Thus
()
[]
()
[]
0214.0%89.1 m
kg
4.21%89.1%595.03%617.03 3
2
1
2
2
2
1
2
2
±=±==
±=±=×−+±=−+±=
ρ
ρρ
uu
uuuu
SG
Dm
Finally, 1) to(20 0214.013.1SG
1) to(20kg/m4.211130 3
±=
±=
ρ