Question

a physical quantity x is calculated from the relation x =a²* b/ √c if the percentage error of measurement a,b,c are 4% ,5% and 9% respectively. find the percentage error of x​

Answer 1

Given :

A physical quantity x is given by

• $\boxed{\bf{\red{x=\dfrac{a^2b}{\sqrt{c}}}}}$

% error in measurement of a = 4%

% error in measurement of b = 5%

% error in measurement of c = 9%

To Find :

We have to find percentage error in x.

Solution :

$\leadsto\sf\:x=\dfrac{a^2b}{\sqrt{c}}$

$\leadsto\sf\:\%\dfrac{\Delta{x}}{x}=\%\dfrac{2\Delta{a}}{a}+\%\dfrac{\Delta{b}}{b}+\%\dfrac{\Delta{c}}{2c}$

$\leadsto\sf\:\%\dfrac{\Delta{x}}{x}=2(4\%)+(5\%)+\dfrac{(9\%)}{2}$

$\leadsto\sf\:\%\dfrac{\Delta{x}}{x}=(8\%)+(5\%)+(4.5\%)$

$\leadsto\bf\:\%\dfrac{\Delta{x}}{x}=17.5\%$

Cheers!