Question

A physical quantity is related to three measureable quantities x, y and z as P = (x^4 y^2)/ z^3. The errors in the measurement of x, y and z are 1%, 2% and 3% respectively. The maximum possible percentage error in the value of P will be

Answer 1

therefore :

t = ∆

$\frac{tx}{x} \times 100 = + - (2\frac{ta}{a} + 3 \frac{tb}{b} + \frac{5}{2 } \frac{tc}{c} + 2 \frac{td}{t} ) \times 100$

$= + - \frac{100}{100}(2 + 6 + \frac{15}{2} + 8)$

$\frac{tx}{x} \times 100 = + - (16 + \frac{15}{2}$

$= + - ( \frac{32 + 15}{2} )$

$= + - \frac{47}{2}$

$= + - 23.5\%$

$mean \: absolute \: earor \:$

$= + - \frac{23.5}{100} = + - 0.235$

$= 0.24$

= 0.24 ( rounding off significant figured)

again rounding off x = 2.763 in two

significant figured = 2.8