WBJEE · Physics · Mathematics in Physics
Given : The percentage error in the measurements of \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) and \(\mathrm{D}\) are respectively, \(4 \%, 2 \%, 3 \%\) and \(1 \%\). The relative error in \(Z=\frac{A^4 B^{\frac{1}{3}}}{C D^{\frac{3}{2}}}\) is
- A \(\frac{127}{2} \%\)
- B \(\frac{127}{5} \%\)
- C \(\frac{127}{6} \%\)
- D \(\frac{127}{7} \%\)
Answer & Solution
Correct Answer
(C) \(\frac{127}{6} \%\)
Step-by-step Solution
Detailed explanation
\quad \mathrm{Z}=\frac{\mathrm{A}^4 \mathrm{~B}^{\frac{1}{3}}}{\mathrm{CD}^{\frac{3}{2}}}=\frac{\Delta \mathrm{Z}}{\mathrm{Z}}=4 \frac{\Delta \mathrm{A}}{\mathrm{A}}+\frac{1}{3} \frac{\Delta \mathrm{B}}{\mathrm{B}}+\frac{\Delta \mathrm{C}}{\mathrm{C}}+\frac{3}{2} \frac{\Delta…
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