Question

A physical quantity X is connected from x=ab2/c . Calculate the percentage error in x , when percentage error in a,b,c are 4,2 and 3 respectively.

Answer 1

Explanation:

hope this helps you to understand

Answer 2

Therefore the percentage error in X is 5%.

Given:

A physical quantity X is related as X =ab²/c

Percentage error in 'a' = 4%

Percentage error in 'b' = 2%

Percentage error in 'c' = 3%

To Find:

The percentage error in X.

Solution:

The given question can be solved as shown below.

The given relation: X =ab²/c

Taking log on both sides,

⇒ log X = log ( ab²/c )

⇒ log X = log a + log b² - log c  

( ∵ log ab = log a + log b and log ( a/b ) = log a - log b )

⇒ log X = log a + 2log b - log c

Now differentiating on both sides,

⇒ d ( log X ) / dx = d ( log a ) / dx + 2d ( log b ) / dx - d ( log c ) / dx

⇒ dX/X = da/a + 2db/b - dc/c

Multiplying both sides with 100

⇒ dX/X × 100 = da/a × 100 + 2db/b × 100 - dc/c × 100

Percentage error in 'x' = dX/X × 100

Percentage error in 'a' = da/a × 100 = 4

Percentage error in 'b' = db/b × 100 = 2

Percentage error in 'c' = dc/c × 100 = 3

⇒ Percentage error in 'x' = dX/X × 100 = 4 + ( 2 × 2 ) - 3

⇒ Percentage error in 'x' = dX/X × 100 = 4 + 4 - 3 = 5

Therefore the percentage error in X is 5%.

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