Question

The physical quantity p is related to four
obserwables a, b,c andd as follows
P=a³b²/√cd

The percentage errors in the measurement of
a, b, c and are 1%,3%, 4% and 2%. respectively
What is the percentage error in the quantity P?
​

Answer 1

Answer:

$\boxed{\mathfrak{Percentage \ error \ in \ quantity \ P = 13\%}}$

Explanation:

According to the question:

$\rm \dfrac{\Delta a}{a} \times 100 = 1 \%$

$\rm \dfrac{\Delta b}{b} \times 100 = 3 \%$

$\rm \dfrac{\Delta c}{c} \times 100 = 4 \%$

$\rm \dfrac{\Delta d}{d} \times 100 = 2 \%$

$\rm P = \dfrac{ {a}^{3} {b}^{2} }{ \sqrt{c} d}$

So,

$\rm \implies \dfrac{\Delta P }{ P } \times 100 = 3\dfrac{\Delta a }{ a } \times 100 + 2 \dfrac{\Delta b}{ b} \times 100 + \dfrac{1}{2} \dfrac{\Delta c}{ c} \times 100 + \dfrac{\Delta d }{ d} \times 100 \\ \\ \rm \implies \dfrac{\Delta P }{ P } \times 100 = 3 \times 1\% + 2 \times 3\% + \dfrac{1}{2} \times 4\% + 2\% \\ \\ \rm \implies \dfrac{\Delta P }{ P } \times 100 = 3\% + 6\% + 2\% + 2\% \\ \\ \rm \implies \dfrac{\Delta P }{ P } \times 100 = 13\%$