A physical quantity P depends on other physical quantities - - - as P - -2 -3-4 where - - and - are known to have maximum percentage errors of 1- 2- and 1- respectively - then maximum percentage error in P would be

Maximum percentage error in P is given by Δ PP = 2 Δαα + 3 Δββ + 4 Δγγ Substituting the data given in the question, Δ PP = ((2 × 1) + (3 × 2) + (4 × 1))% ⇒Δ P ...

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Byju's Answer

Standard XII

Physics

Addition & Subtraction of Errors

A physical qu...

Question

A physical quantity $P$ depends on other physical quantities $α, β, γ$ as $P = \frac{α^{2} β^{3}}{γ^{4}}$ where $α, β,$ and $γ$ are known to have maximum percentage errors of $1 %, 2 %$ and $1 %$ respectively , then maximum percentage error in $P$ would be

4 %

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10 %

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12 %

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6 %

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Solution

The correct option is C $12 %$
Maximum percentage error in $P$ is given by
$\frac{Δ P}{P} = 2 \frac{Δ α}{α} + \frac{3 Δ β}{β} + \frac{4 Δ γ}{γ}$

Substituting the data given in the question,

$\frac{Δ P}{P} = ((2 \times 1) + (3 \times 2) + (4 \times 1)) %$
$\Rightarrow \frac{Δ P}{P} = 12 %$

Hence, option $(c)$ is correct.

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A physical quantity P depends on other physical quantities α,β,γ as P=α2β3γ4 where α,β, and γ are known to have maximum percentage errors of 1%,2% and 1% respectively , then maximum percentage error in P would be

The correct option is C 12%Maximum percentage error in P is given by ΔPP=2Δαα+3Δββ+4Δγγ Substituting the data given in the question, ΔPP=((2×1)+(3×2)+(4×1))% ⇒ΔPP=12% Hence, option(c) is correct.

A physical quantity $P$ depends on other physical quantities $α, β, γ$ as $P = \frac{α^{2} β^{3}}{γ^{4}}$ where $α, β,$ and $γ$ are known to have maximum percentage errors of $1 %, 2 %$ and $1 %$ respectively , then maximum percentage error in $P$ would be