A physical quantity x is calculated from the relation x = a 2 b 3 c d . If percentage error in a , b , c and d are 2 % , 1 % , 3 % and 4 % , respectively. What is the percentage error in x ?

∆ X X = ± 2 ∆ a a + 3 ∆ b b + ∆ c c + ∆ d 2 d = ± 2 × 2 + 3 × 1 + 3 + 1 2 × 4 = ± 12 %

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Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousEasy2 minPYQ_2020

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A physical quantity $x$ is calculated from the relation $x = \frac{a^{2} b^{3}}{c \sqrt{d}}$ . If percentage error in $a, b,$ $c$ and $d$ are $2 %, 1 %, 3 %$ and $4 %$ , respectively. What is the percentage error in $x$ ?

Options:

Answer:

Solution:

$\frac{∆ X}{X} = \pm (\frac{2 ∆ a}{a} + \frac{3 ∆ b}{b} + \frac{∆ c}{c} + \frac{∆ d}{2 d})$

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

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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