A physical quantity Q is calculated according to the expression Q=A3B3CDIf percentage errors in A, B, C, D are 2%, 1 %, 3% and 4%, respectively. What is the percentage error in Q?

dQQ=3⋅dAA+3⋅dBB+dCC+12⋅d(D)D=3⋅(2%)+3⋅(1%)+1(3%)+12×(4%)=14%

A physical quantity Q is calculated according to the expression Q=A3B3CDIf percentage errors in A, B, C, D are 2%, 1 %, 3% and 4%, respectively. What is the percentage error in Q?

dQQ=3⋅dAA+3⋅dBB+dCC+12⋅d(D)D=3⋅(2%)+3⋅(1%)+1(3%)+12×(4%)=14%

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A physical quantity Q is calculated according to the expression
$Q = \frac{A^{3} B^{3}}{C \sqrt{D}}$
If percentage errors in A, B, C, D are 2%, 1 %, 3% and 4%, respectively. What is the percentage error in Q?

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± 8%

± 10%

± 14%

± 12%

answer is C.

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$\begin{aligned} \frac{dQ}{Q} = 3 \cdot \frac{dA}{A} + 3 \cdot \frac{dB}{B} + \frac{dC}{C} + \frac{1}{2} \cdot \frac{d (D)}{D} \\ = 3 \cdot (2 %) + 3 \cdot (1 %) + 1 (3 %) + \frac{1}{2} \times (4 %) \\ = 14 % \end{aligned}$

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A physical quantity Q is calculated according to the expression Q=A3B3CDIf percentage errors in A, B, C, D are 2%, 1 %, 3% and 4%, respectively. What is the percentage error in Q?

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A physical quantity Q is calculated according to the expression
$Q = \frac{A^{3} B^{3}}{C \sqrt{D}}$
If percentage errors in A, B, C, D are 2%, 1 %, 3% and 4%, respectively. What is the percentage error in Q?