Question

physical quantity x is calculated from the relation x = a^2 b^3 / cd^1/2 . if percentage error in a, b, c and d are 2%, 1% , 3% and 4%, respectively . what is the percentage error in x ?​ please help me out with this question

Answer 1

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%