2019 Units and MeasurementsErrors in Measurement – Combination of Errors Medium Question 31 of 53 in Units and Measurements

In an experiment, the percentage of error occurred in the measurment of physical quantities $A$, $B$, $C$ and $D$ are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement $X$, where $X=\frac{A^2B^{1/2}}{C^{1/3}D^3}$, will be:

A $\left(\frac{3}{13}\right)\%$
B $16\%$
C $-10\%$
D $10\%$

The answer is B.

Solution

$X=\frac{A^2B^{1/2}}{C^{1/3}D^3}$ Maximum % error: $\frac{\Delta X}{X}\times100=2\frac{\Delta A}{A}\times100+\frac{1}{2}\frac{\Delta B}{B}\times100+\frac{1}{3}\frac{\Delta C}{C}\times100+3\frac{\Delta D}{D}\times100$ $=2(1\%)+\frac{1}{2}(2\%)+\frac{1}{3}(3\%)+3(4\%)$ $=2\%+1\%+1\%+12\%=16\%$

Concept maximum percentage error in a derived quantity

Units and Measurements in past papers

53 questions from this chapter have appeared across 25 exam years.