Question

Errors in sum and difference? A small explanation

the volumes of two bodies are measured to be V1=10.2+/- 0.02

V2= 6.2+/-0.01..calculate the sum and difference in volumes with error differences.

Answer 1

V1 = ( A ± ΔA ) = ( 10.2 ± 0.02 )cm^3
v2 = ( B ± ΔB ) = ( 6.4 ± 0.01 )cm^3

let v3 be the sum of the given volumes
therefore, v3= ( Z ± ΔZ )cm^3
where Z is the true value of the sum and ± ΔZ is the error limit


Z = A + B
= 10.2 + 6.4
= 16.6 cm^3

and ± ΔZ = ± (ΔA + ΔB )
= ± (0.02 +0.01 )
= ± 0.03

therefore, v3 = ( Z ± ΔZ )cm^3 = ( 16.6 ± 0.03 ) cm^3


now, let v4 be the difference of the given volumes.
therefore, v4 = ( X ± ΔX )cm^3

hence,
X = A - B
= 10.2 - 6.4
= 3.8 cm^3

and ± ΔX = ± (ΔA + ΔB )
= ± (0.02 +0.01 )
= ± 0.03

therefore, v4 = ( X ± ΔX )cm^3 = ( 3.8 ± 0.03 ) cm^3