You measure a quantity x and find x = (3.2 ± 0.1)m/s. Calculate the value of q (including the error), where q is given by: q = 1/x
Answers
Explanation:
(Solution)
Solution Assignment: Uncertainties and data
processing
1. Suppose you measure three independent variables as,
x = 10 ± 2, y = 7 ± 1, θ = (40 ± 3)◦
.
based on which you calculate the following quantity,
q =
x + 2
x + y cos(4θ)
,
What would be your answer for q and uncertainty?
Solution:
Given values are:
x = 10 ± 2, y = 7 ± 1, θ = (40 ± 3)◦
.
The mathematical expression for q is,
q =
x + 2
x + y cos(4θ)
=
10 + 2
10 + 7(cos(160◦
))
=
12
10 + 7(−0.939) =
12
3.427
= 3.50
Using Taylor series relationship for finding uncertainty in q,
∆q =
√(
∂q
∂x ∆x
)2
+
(
∂q
∂y ∆y
)2
+
(
∂q
∂θ ∆θ
)2
. (1)
Where,
(
∂q
∂x)
=
[x + y cos(4θ)](1) − (x + 2)(1)
[x + y cos(4θ)]2
=
3.427 − 12
(3.427)2
= −0.732
Answer:
what is the ph value find out