TS EAMCET · Physics · Mathematics in Physics
A quantity \(z\), to be estimated has a dependency on the variables \(a, b\) and \(c\) as \(z=a b^2 c^{-2}\). The percentage of error in the measurement of \(a, b\) and \(c\) are respectively, \(2.1 \%, 1.3 \%\) and \(2.2 \%\). The percentage of error in the measurement of \(z\) would then be
- A \(5.6 \%\)
- B \(1.6 \%\)
- C \(1.0 \%\)
- D \(9.1 \%\)
Answer & Solution
Correct Answer
(D) \(9.1 \%\)
Step-by-step Solution
Detailed explanation
Given, \(z=a b^2 c^{-2}\) So, the percentage error in the volume is given by \(\begin{aligned} & \frac{\Delta z}{z} \times 100=\left[\frac{\Delta a}{a}+2 \frac{\Delta b}{b}+2 \frac{\Delta c}{c}\right] \times 100 \\ & =2.1 \%+2(1.3 \%)+2(2.2 \%)=9.1 \% \end{aligned}\) So, the…
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