Two objects A and B are of lengths 5 cm and 7cm determined with errors 0.1 cm and 0.2 cm respectively.What is the error in determing (a) the total length and (b) the difference in their lengths?

Explanation

a = 5cm, `Delta a=0.1` cm
b=7 cm, `Delta b =0.2cm`
If x =a+ b is the total length, then
`Deltax Deltaa +Deltab =0.1 +0.2 =0.3 cm`
and x =(5+7) `pm` 0.3 = (12`pm`0.3) cm .
If x is the difference between the lengths then
`Deltax = Deltaa +Deltab = 0.3 cm ` and
`x=|5-7|pm 0.3 (2 pm 0.3)cm`