Question

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. The minimum amount of percentage error in the measurement of X is contributed by :

• A. A
• B. B
• C. C
• D. D

Answer 1

The correct option is C C

$X=\frac{A^{2}B}{C^{1/3}{D}^3}$

So, fractional error in the measurement of $X$ is:

$\frac{\Delta X}{X}=\frac{2\Delta A}{A}+\frac{\Delta B}{B}+\frac{1}{3}\frac{\Delta C}{C}+\frac{3\Delta D}{D}$

$=(2\times 2)+2+(\frac{1}{3}\times 4)+(3\times 5)$

$(\frac{1}{3}\times 4\Rightarrow$ Minimum error out of the four)

Hence, minimum error is contributed by C.