Question

If the formula for 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 the percentage error in X.
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Answer 1

Answer:

4(2)+3(3)+1/3(3)+1/2(4)

=8+9+1+2

=20

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Answer 2

the formula for a physical quantity is \bf{x=\frac{a^3b^4}{c^{1/3}d^{1/2}}}

so, fractional error is given as

∆X/X = 3 × (∆a/a) + 4 × (∆b/b) + 1/3 × (∆c/c) + 1/2 × (∆d/d)

[ we know, % error = 100 × fractional error ]

so, percentage error of X is given as ;

% error of X = 3 × % error of a + 4 × % error of b + 1/3 × % error of c + 1/2 × % error of d

given, % error of a = 2% , % error of b = 3% , % error of c = 3% and % error of d = 4%

so, % error of X = 3 × 2 % + 4 × 3% + 1/3 × 3% + 1/2 × 4%

= 6% + 12% + 1% + 2%

= 21%

hence, percentage error of X = 21 %

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