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Two objects A and B are of lengths 5 cm ...

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?

Text Solution

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