the mass of solid sphere is measured to be (1.85+_0.05)kg and its radius to be (5.62+_0.20)cm. calculate its density (in kg/m3) to the correct no of significant figures and the uncertainty in the density.
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Answer:
r=(6.50±0.20)cm=(6.50±0.20)∗10
−2
m
m=(1.85+0.02)kg
ρ=
(
3
4
)πr
3
m
also,
ρ
δρ
=
m
δm
+
r
3δr
In other words, the percentages of uncertainty are cumulative.
Therefore,
ρ
δρ
=
1.85
0.02
+
6.50
3(0.20)
=0.103,
ρ=
(
3
4
)π(6.5∗10
−2
m)
3
1.85
=1.61∗10
3
kg/m
3
then δρ=0.103ρ=0.166∗10
3
kg/m
3
and ρ±δρ=(1.61±0.17)∗10
3
kg/m
3
=(1.6±0.2)∗10
3
kg/m
3
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