TS EAMCET · Physics · Mathematics in Physics
In the measurement of a physical quantity \(X=\frac{A^2 B}{C^{1 / 3} D^3}\). The percentage errors introduced in the measurements of the quantities \(A, B, C\), and \(D\) are \(2 \%, 2 \%, 4 \%\) and \(5 \%\), respectively. Then, the minimum amount of percentage error in the measurement of \(X\) is contributed by
- A \(A\)
- B \(B\)
- C \(C\)
- D \(D\)
Answer & Solution
Correct Answer
(C) \(C\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & x=\frac{A^2 B}{C^{1 / 3} D^3} \\ & \% \text { error in } x, \\ & \frac{\Delta x}{x}=2 \frac{\Delta A}{A}+\frac{\Delta B}{B}+\frac{1}{3} \frac{\Delta C}{C}+\frac{3 \Delta D}{D} \\ & 2\left(\frac{\Delta A}{A} \times 100 \%\right)+\left(\frac{\Delta B}{B} \times…
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