Question

An experiment measured quantities a,b,c and then x is calculated by using the relation x = ab2 / c3 . If the percentage errors in measurements a.b,and c are ± 1%, ± 2% and ± 1.5% respectively, then calculate the maximum percentage error in value of x obtained.

Answer 1

Given that,

Percentage error in measurements

$\dfrac{\Delta a}{a}= \pm 1\%$

$\dfrac{\Delta b}{b}= \pm 2\%$

$\dfrac{\Delta c}{c}= \pm 1.5\%$

The relation is

$x=\dfrac{ab^2}{c^3}$

We need to calculate the maximum percentage error in value of x

Using given relation

$x=\dfrac{ab^2}{c^3}$

$\dfrac{\Delta x}{x}=\dfrac{\Delta a}{a}+2\dfrac{\Delta b}{b}+3\dfrac{\Delta c}{c}$

Put the value into the formula

$\dfrac{\Delta x}{x}=\pm 1+2\times\pm 2+3\times\pm 1.5$

$\dfrac{\Delta x}{x}=\pm 9.5\%$

Hence, The maximum percentage error in value of x is  ±9.5%.

Answer 2

Answer:  +-9.5%

Hope it helps :)