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Physics
Physics
Problem
When two measured quantities
x
x
x
and
y
y
y
with absolute uncertainties
Δ
x
\Delta x
Δ
x
and
Δ
y
\Delta y
Δ
y
are added to obtain
z
=
x
+
y
z = x + y
z
=
x
+
y
, the absolute uncertainty
Δ
z
\Delta z
Δ
z
in
z
z
z
is a)
Δ
z
=
Δ
x
2
+
Δ
y
2
\Delta z = \sqrt{\Delta x^{2} + \Delta y^{2}}
Δ
z
=
Δ
x
2
+
Δ
y
2
b)
Δ
z
=
z
(
Δ
x
x
+
Δ
y
y
)
\Delta z = z\!\left(\dfrac{\Delta x}{x}+\dfrac{\Delta y}{y}\right)
Δ
z
=
z
(
x
Δ
x
+
y
Δ
y
)
c)
Δ
z
=
Δ
x
+
Δ
y
\Delta z = \Delta x + \Delta y
Δ
z
=
Δ
x
+
Δ
y
d)
Δ
z
=
Δ
x
+
Δ
y
2
\Delta z = \dfrac{\Delta x + \Delta y}{2}
Δ
z
=
2
Δ
x
+
Δ
y
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