Question

A physical quantity P is related to four observables a,b,c and d as follows P=a3b2(√cd). The percentage error in measuring a,b,c,d are 1%,3%,4% and 2% respectively. What is percentage error in calculation of P

Answer 1

that's the answer hope it helps you

Answer 2

Answer:

The percentage error in P is 13%.

Explanation:

Given that,

$P=a^3b^2(\sqrt{c}d)$

a = 1%

b= 3%

c=4%

d=2%

The percentage error in P

$\dfrac{\Delta P}{P}\times100=[3\times\dfrac{\Delta a}{a}+2\times\dfrac{\Delta b}{b}+\dfrac{1}{2}\dfrac{\Delta C}{C}+\dfrac{\Delta d}{d}]\times100$

$\dfrac{\Delta P}{P}\times100=[3\times\dfrac{1}{100}+2\times\dfrac{3}{100}+\dfrac{1}{2}\times\dfrac{4}{100}+\dfrac{2}{100}]\toimes100$

$\dfrac{\Delta P}{P}\times100=[\dfrac{3+6+2+2}{100}]\times100$

$\dfrac{\Delta P}{P}\times100=[\dfrac{13}{100}]\times100$

$\dfrac{\Delta P}{P}\times100=13\%$

Hence, The percentage error in P is 13%.