What is the percentage error in the physical quantity A If it is related to four other physical quantities a , b , c and d as A = a 2 b 3 d c ? The percentage error in measurement of a , b , c and d are 1 % , 3 % , 2 % and 1 % respectively.

Percentage error in A = 2 Δ a a + 3 Δ b b + 1 2 Δ c c + Δ d d = 2 × 1 + 3 × 3 + 1 2 × 2 + 1 × 1 % = 13 %

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PhysicsPractical physicsMiscellaneousEasy2 minQB

PhysicsEasynumerical

What is the percentage error in the physical quantity $A$ If it is related to four other physical quantities $a$ , $b$ , $c$ and $d$ as $A = \frac{a^{2} b^{3}}{d \sqrt{c}}$ ? The percentage error in measurement of $a$ , $b$ , $c$ and $d$ are $1 %$ , $3 %$ , $2 %$ and $1 %$ respectively.

Answer:

13.00

Solution:

Percentage error in $A$

$= 2 \frac{Δ a}{a} + 3 \frac{Δ b}{b} + \frac{1}{2} \frac{Δ c}{c} + \frac{Δ d}{d}$

$= (2 \times 1 + 3 \times 3 + \frac{1}{2} \times 2 + 1 \times 1) % = 13 %$

Stream:JEESubject:PhysicsTopic:Practical physicsSubtopic:Miscellaneous

⏱ 2mℹ️ Source: QB

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