The physical quantity X is related to three quantities a, b, and c as X = a²b³ c¹/². The percentage error in magnitude of a, b, c are 1%, 2% and 4% respectively. What is the percentage error in X?
6%
14%
10%
9%
Answers
Answered by
2
Given x=
c
1/2
d
1/2
a
3
b
2
On taking log and differentiating, we get
x
Δx
=3
a
Δa
+2
b
Δb
+(
2
1
)
c
Δc
+(
2
1
)
d
Δd
⇒ Percentage error in x=3(1)+2(3)+
2
1
(4)+
2
1
(2)=12%
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2
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