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Solve the numerical example. If the formula for a physical quantity is X = a4b3c1/3d1/2 and if the percentage error in the measurements of a, b, c and d are 2%, 3%, 3% and 4% respectively. - Physics

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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.

Numerical

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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Chapter 1: Units and Measurements - Exercises [Page 15]

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Balbharati Physics [English] 11 Standard Maharashtra State Board
Chapter 1 Units and Measurements
Exercises | Q 3. xiv) | Page 15

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