Question

In a measurement, the uncertainty of length $L$ is $\pm a$ and the uncertainty of width $W$ is $\pm b$. Assuming a and b very small, find the the uncertainty in measurement of area.

• A. $a/L+b/W$
• B. $aL+bW$
• C. $aW+bL$
• D. $a^2/W+b^2/L$

Answer 1

Answer: (C)

$aW+bL$

Here given, $\Delta L=a$ and $\Delta W=b$
Area, $A=LW$
Take ln and then differentiate, $\frac{\Delta A}{A}=\frac{\Delta L}{L}+\frac{\Delta W}{W}=a/L+b/W$
So,$\Delta A=(a/L+b/W)\left(LW\right)=aW+bL$