Two objects `A` and `B` are of lengths `5cm` and `7cm` determined with errors `0.1cm` and `0.2cm` respecitively. The error in determining (a) the total length and (b) the difference in their lengths are

Explanation

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