Question

A physical quantity a is related to four observable x y z and m as follows A equal to xy/mz the percentage errors of measures in x y z and m are 4 % 3% 2% and 1% respectively what is the percentage error in the quantity A

Answer 1

Answer:

Given:

A relationship has been provided as follows :

$\boxed{ \huge{ \sf{a = \dfrac{xy}{mz}}}}$

To find:

Max error in "a" when error of each quantity has been given.

Concept:

Max error can be found by adding the error of each quantity multiplied with the respective exponential in the given Equation.

Calculation:

$\boxed{ \sf{ \red{ \frac{ \Delta a}{a} = \dfrac{ \Delta x}{x} + \dfrac{ \Delta y}{y} + \dfrac{ \Delta m}{m} + \dfrac{ \Delta z}{z}}}}$

$\sf{ \implies \dfrac{ \Delta a}{a} = 4 + 3 + 1 + 2}$

$\sf{ \implies \dfrac{ \Delta a}{a} = 10\%}$

So final answer :

$\boxed{ \sf{max \: error = 10\%}}$

Additional information:

• For max error , always add the individual errors.
• Remember to Multiply each term with exponential (here exponential was 1)
• Express the final answer in percentage.

Answer 2

$\blue{\underline{ \huge{ \blue{\boxed{ \mathfrak{\fcolorbox{red}{orange}{\purple{Answer}}}}}}}} \\ \\ \star \rm \: \blue{Given} \\ \\ \leadsto \rm \: physical \: quantity \: A \: is \: represented \: as \\ \\ \: \: \: \: \: \: \: \: \: \: \: \boxed{\bold{ \red{ \rm{A = \frac{xy}{mz} }}}}\\ \\ \star \rm \: \blue{To \: Find} \\ \\ \leadsto \rm \: max \: error \: in \: A.... \\ \\ \star \rm \: \blue{Formula \: and \: Calculation} \\ \\ \leadsto \rm \: \orange{\% \frac{ \triangle{A}}{A} = \% \frac{ \triangle{x}}{x} + \% \frac{ \triangle{y}}{y} + \% \frac{ \triangle{m}}{m} + \frac{ \triangle{z}}{z} } \\ \\ \leadsto \rm \: \% \frac{ \triangle{A}}{A} = 4\% + 3\% + 2\% + 1\% \\ \\ \star \: \boxed{ \pink{ \bold{ \rm{\% \frac{ \triangle{A}}{A} = 10\%\:(max.\: error)}}}} \: \star$