JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
A physical quantity \(P\) is given as \(P=\frac{a^2 b^3}{c \sqrt{d}}\) The percentage error in the measurement of \(a, b, c\) and \(d\) are \(1 \%, 2 \%, 3 \%\) and \(4 \%\) respectively. The percentage error in the measurement of quantity \(P\) will be \(.......\%\)
- A \(13\)
- B \(14\)
- C \(12\)
- D \(16\)
Answer & Solution
Correct Answer
(A) \(13\)
Step-by-step Solution
Detailed explanation
\(\frac{\Delta P }{ P } \times 100 \%=\left(2 \frac{\Delta a }{ a }+3 \frac{\Delta b }{ b }+\frac{\Delta c }{ c }+\frac{1}{2} \frac{\Delta d }{ d }\right) \times 100 \%\) \(=2(1 \%)+3(2 \%)+3 \%+\frac{1}{2} \times 4 \%=13 \%\)
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