Question

q=b*(a-c). the percentage error in measurement of b is 1%, c is 2% and a is 3%. what is the percentage error in measurements?

Answer 1

As we have learned

Error in quantity raised to some power -

x=\frac{a^{n}}{b^{m}}\rightarrow \frac{\Delta x}{x}=\pm \left ( n\frac{\Delta a}{a}+m\frac{\Delta b}{b} \right )

- wherein

\Delta a= absolute error in measurement of a

\Delta b= absolute error in measurement of b

\Delta x= absolute error in measurement of x

 

\frac{\Delta P }{P} 100 \%= 0.5     \frac{\Delta Q}{Q}\times 100\%= 1

\frac{\Delta R}{R}\times 100\%= 3   \frac{\Delta S}{S}\times 100\% =1.5  

 

\frac{\Delta A}{A}\times 100\% =3\frac{\Delta P}{P}\times 100\%+2\frac{\Delta Q}{Q}\times 100\%+1/2 \frac{\Delta R}{R}\times 100\%+\frac{\Delta S}{S}\times 100\%

= 3\times 0.5+2\times 1+1/2\times 3+1.5=6.5 \%