Question

A physical quantity X is calculated from the relation c d a b X 2 3  . if the percentage error in a, b, c and d are 2%, 1%, 3% and 4% respectively. Find the percentage 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%