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