Question

The physical quantity X is related to three quantities a, b, and c as X = a²b³ c¹/². The percentage error in magnitude of a, b, c are 1%, 2% and 4% respectively. What is the percentage error in X?



6%

14%

10%

9%

​

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%

Answer 2

Answer:

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