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