A physical quantity P is related to four observations, a, b, c and d as follows: P=a3b2c√d.P=a3b2cd. The percentage errors of measurements in a, b, c and d are 1%, 3%, 4% and 2% respectively. The percentage error in the quantity P is
Answers
Answer:
The percentage error in P is 13%.
Explanation:
Given that,
P=a^3b^2(\sqrt{c}d)P=a
3
b
2
(
c
d)
a = 1%
b= 3%
c=4%
d=2%
The percentage error in P
\dfrac{\Delta P}{P}\times100=[3\times\dfrac{\Delta a}{a}+2\times\dfrac{\Delta b}{b}+\dfrac{1}{2}\dfrac{\Delta C}{C}+\dfrac{\Delta d}{d}]\times100
P
ΔP
×100=[3×
a
Δa
+2×
b
Δb
+
2
1
C
ΔC
+
d
Δd
]×100
\dfrac{\Delta P}{P}\times100=[3\times\dfrac{1}{100}+2\times\dfrac{3}{100}+\dfrac{1}{2}\times\dfrac{4}{100}+\dfrac{2}{100}]\toimes100
P
ΔP
×100=[3×
100
1
+2×
100
3
+
2
1
×
100
4
+
100
2
]\toimes100
\dfrac{\Delta P}{P}\times100=[\dfrac{3+6+2+2}{100}]\times100
P
ΔP
×100=[
100
3+6+2+2
]×100
\dfrac{\Delta P}{P}\times100=[\dfrac{13}{100}]\times100
P
ΔP
×100=[
100
13
]×100
\dfrac{\Delta P}{P}\times100=13\%
P
ΔP
×100=13%
Hence, The percentage error in P is 13%.
Explanation:
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