Question

9. In an experiment, the percentage of error occurred
in the measurement of physical quantities A, B, C
and D are 1%, 2%, 3% and 4% respectively. Then
the maximum percentage of error in the
meagurement X. where x = A^2B^1/2/C^1/3D^3 , will be​

Answer 1

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Answer 2

Given that,

The measurement in X is given by :

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

The percentage of error occurred  in the measurement of physical quantities A, B, C  and D are 1%, 2%, 3% and 4% respectively.

To find,

The maximum percentage of error is X.

Solution,

The percentage error in X is given by :

$\dfrac{\Delta X}{X}=2\dfrac{\Delta A}{A}+\dfrac{1}{2}\dfrac{\Delta B}{B}+\dfrac{1}{3}\dfrac{\Delta C}{C}+3\dfrac{\Delta D}{D}\\\\\dfrac{\Delta X}{X}=2\times 1+\dfrac{1}{2}\times 2+\dfrac{1}{3}\times 3+3\times 4\\\\\dfrac{\Delta X}{X}=16\%$

So, the maximum percentage of error in the  measurement X is 16 %.

Learn more,

Percentage error

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