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Question

A physical quantity, y=a4b2(cd4)1/3 has four observables a, b, c and d. The percentage error in a, b, c and d are 2%,3% 4% and 5% respectively the error in y will be

A
6%
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B
11%
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C
12%
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D
22%
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Solution

The correct option is D 22%
Here y=a4b2(cd4)1/3
Taking log on both sides, we get
log y = 4 log a + 2 log b -13 log c - 43 log d
Differentiating both sides to calculate error,
Δyy×100=4(Δaa×100)+2(Δdd×100)+13(Δcc×100)+43(Δdd×100)=[4×2%+2×3%+13×4%+43×5%]=22%

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