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Question
Solve the numerical example.
If the formula for a physical quantity is X = `("a"^4"b"^3)/("c"^(1//3)"d"^(1//2))` and if the percentage error in the measurements of a, b, c and d are 2%, 3%, 3% and 4% respectively. Calculate percentage error in X.
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Solution
Given: X = `("a"^4"b"^3)/("c"^(1//3)"d"^(1//2))`
The percentage error in a, b, c, d is respectively 2%, 3%, 3% and 4%.
`(Δ"x")/"x" xx 100` = 4 × % error of a + 3 × % error of b + `1/3` × % error of c + `1/2` × % error of d
i.e. X `= [(4 xx 2) + (3 xx 3) + (1/3 xx 3) + (1/2 xx 4)]`
Percentage error in X = [8 + 9 + 1 + 2] = 20%
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