Question

Physical quantity P is related to three observables a,b and c as P=√ab²/c². The error in

measurement of a,b and c are 2%,2% and 3% respectively. What is the Percentage error in the

quantity P?​

Answer 1

Answer:

Given;

$\longrightarrow\rm P = \dfrac{\sqrt{a} \: b^2}{c^2}$

• We need to find the percentage error in the quantity P.

Calculation:

$\longrightarrow\rm \dfrac{\Delta P}{P} \times 100= \dfrac{1}{2} \Bigg(\dfrac{\Delta a}{a} \Bigg)\times 100 + 2\Bigg(\dfrac{\Delta b}{b} \Bigg)\times 100 + 2\Bigg(\dfrac{\Delta c}{c} \Bigg)\times 100$

$\longrightarrow\rm \dfrac{\Delta P}{P} \times 100= \dfrac{1}{2} \times 2\% + 2 \times 2\% + 2 \times 3\%$

$\longrightarrow\rm \dfrac{\Delta P}{P} \times 100= 1 \% + 4\% + 6\%$

$\longrightarrow\bf \dfrac{\Delta P}{P} \times 100= 11\%$

Answer 2

I hope this is help full to you