Question

A physical quantity Z is related to three observables a,b and c as Z=[ab^1/3]/c^-2
The maximum percentage error in a=2% , b=3% and c=1%
so the maximum % error in Z?
(when multiplying c % error with its power do we take -2 or only 2?)

Answer 1

Explanation:

The given physical quantity A=

c

d

a

2

b

3

Given :

a

Δa

×100=1%,

b

Δb

×100=3%,

c

Δc

×100=2% and

d

Δd

×100=2%

Percentage error in A,

A

ΔA

×100= 2

a

Δa

×100 +3

b

Δb

×100 +

c

Δc

×100+

2

1

×

d

Δd

×100

⟹

A

ΔA

×100=2×1+3×3+2+

2

1

×2=14 %