5. A physical quality I The percentage error of measurement in a, b, c and d are 1%, 2%, 3%, and 4% respectively. What is the percentage error in the quantity P? [Ans. 13%]
Answers
Answer:
=cda3b2
=cda3b2Maximum fractional error in P is given by
=cda3b2Maximum fractional error in P is given byPΔP=±[3aΔa+2bΔb+21cΔc+dΔd]
=cda3b2Maximum fractional error in P is given byPΔP=±[3aΔa+2bΔb+21cΔc+dΔd]On putting above value:
=cda3b2Maximum fractional error in P is given byPΔP=±[3aΔa+2bΔb+21cΔc+dΔd]On putting above value: =±10013=0.13
=cda3b2Maximum fractional error in P is given byPΔP=±[3aΔa+2bΔb+21cΔc+dΔd]On putting above value: =±10013=0.13Percentage error in P=13 %
=cda3b2Maximum fractional error in P is given byPΔP=±[3aΔa+2bΔb+21cΔc+dΔd]On putting above value: =±10013=0.13Percentage error in P=13 %Value of P is given as 3.763.
=cda3b2Maximum fractional error in P is given byPΔP=±[3aΔa+2bΔb+21cΔc+dΔd]On putting above value: =±10013=0.13Percentage error in P=13 %Value of P is given as 3.763.By rounding off the given value to the first decimal place, we get P=3.8.
Answer:
The percentage error in P is 13%.
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:
Thank you for the points.