Question

You measure two quantities as A=5.7 m ± 0.1 m, B=3.4 m ± 0.2 m. The correct value for AB as?

Answer 1

Given that,

A = 5.7 m ± 0.1 m

B = 3.4 m ± 0.2 m

Suppose we find the value of $\sqrt{AB}$

We need to calculate the value of Y 

Using formula for real term

$Y=\sqrt{AB}$

Put the value into the formula

$Y=\sqrt{5.7\times3.4}$

$Y=4.40$

We need to calculate the value of  error $\dfrac{\Delta Y}{Y}$

Using formula for error

$\dfrac{\Delta Y}{Y}=\dfrac{1}{2}\times\dfrac{\Delta A}{A}+\dfrac{1}{2}\times\dfrac{\Delta B}{B}$

Put the value into the formula

$\dfrac{\Delta Y}{19.38}=\dfrac{1}{2}\times\dfrac{0.1}{5.7}+\dfrac{1}{2}\times\dfrac{0.2}{3.4}$

$\Delta Y= 4.40\times0.0381$

$\Delta Y=0.2$

We need to calculate the value of √AB with error

Using formula for √AB

$\sqrt{AB}=Y+\Delta Y$

Put the value in to the formula

$\sqrt{AB}=4.40\pm 0.2$

Hence, The value of AB is $4.40\pm 0.2$