NEET · Physics · STD 11 - 1. units,dimensions and measurement
A physical quantity \(P\) is related to four observations \(a, b, c\) and \(d\) as follows:
\(P=a^3 b^2 / c \sqrt{d}\)
The percentage errors of measurement in \(a, b, c\) and \(d\) are \(1 \%, 3 \%, 2 \%\) and \(4 \%\) respectively. The percentage error in the quantity \(P\) is
- A \(10 \%\)
- B \(2 \%\)
- C \(13 \%\)
- D \(15 \%\)
Answer & Solution
Correct Answer
(C) \(13 \%\)
Step-by-step Solution
Detailed explanation
\(P=a^3 b^2 c^{-1} d^{-1 / 2} \)
\( \left(\frac{\Delta P}{P} \times 100\right)=\left(\frac{3 \Delta a}{a}+\frac{2 \Delta b}{b}+\frac{1 \Delta c}{c}+\frac{1}{2} \frac{3 \Delta d}{d}\right) \times 100 \)
\( =3(1 \%)+2(3 \%)+1(2 \%)+\frac{1}{2}(4 \%) \)
\( =13 \%\)
\( \left(\frac{\Delta P}{P} \times 100\right)=\left(\frac{3 \Delta a}{a}+\frac{2 \Delta b}{b}+\frac{1 \Delta c}{c}+\frac{1}{2} \frac{3 \Delta d}{d}\right) \times 100 \)
\( =3(1 \%)+2(3 \%)+1(2 \%)+\frac{1}{2}(4 \%) \)
\( =13 \%\)
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