Question

A physical quantity x is given by x = a2b 3 /cd , if the percentage errors of measurement in a,b,c and d are 4%,2%,3% and 1% respectively, then calculate the % error in x.

Answer 1

Answer:

Given x=

c

1/2

d

1/2

a

3

b

2

On taking log and differentiating, we get

x

Δx

=3

a

Δa

+2

b

Δb

+(

2

1

)

c

Δc

+(

2

1

)

d

Δd

⇒ Percentage error in x=3(1)+2(3)+

2

1

(4)+

2

1

(2)=12%