Question

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

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

error in the measurement $X$ will be

Accepted Answer

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

$$\% 	ext{ error, } \frac{\Delta x}{x} 	imes 100 = 2 \frac{\Delta A}{A} 	imes 100 + \frac{1}{2} \frac{\Delta B}{B} 	imes 100 + \frac{1}{3} \frac{\Delta C}{C} 	imes 100 + 3 \frac{\Delta D}{D} 	imes 100$$

$$= 2 	imes 1\% + \frac{1}{2} 	imes 2\% + \frac{1}{3} 	imes 3\% + 3 	imes 4\%$$

$$= 2\% + 1\% + 1\% + 12\%$$

$$= 16\%$$

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